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A1228 指数Riordan阵列(1,x(1+x/2))。 十八

%i

%s1,01,1,1,0.1,1,0.1,0.1,0.1,0.61,0.1,0.1,0.01,0.1,0.01,0.1,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.1,0.61,0.1,0.61,0.1,0.61,0.1,0.01,0.01,0.01,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,

%T 105105、21、1、0、0、0、01054、202、10、28、1、0、0、0、0、0、0945 126037、36、1 0、

%u,0,0942525315630,45,1,0,0,0,0,01030517325693099055,1,0.

%n指数Riordon阵列(1,x(1+x/2))。

%C项是贝塞尔多项式系数。行和是A000 00 85。对角线和是A1228 49。逆是A12850。A000 7318和A1228 48的产品给出了A100862。

%C T(n,k)是{1,2,…,n}具有完全k个循环的自逆排列的数目。-杰弗里克里特兹,五月08日2012

第二类的%C贝塞尔数。对于Hermite多项式和加泰罗尼亚(A033 184和A000 97 66)和斐波那契(A011973,A098925和A09865)矩阵的关系,见杨和乔。12月18日,2013。

%c也是奇数乘积{=0…n-1 }(2×k+ 1)(a00 1147)的双阶乘的逆贝尔变换。对于贝尔变换的定义见A26428和交叉引用A265604。-彼得卢斯尼耶夫,12月31日2015

%H G. C. Greubel,< HREF=“/A1228 48 /B1228 48 .txt”> n表,a(n)为前50行,平坦化</a>

% H P. Bala,< HREF=“/A03532/A03532.TXT”>广义Dobnsik公式</a>

%H Richell O. Celeste,Roberto B. Corcino,肯约法尼尔M冈萨雷斯。< HREF=“http://www. EMIS.AMS.Org/Jeals/JIS/Vor20/Celeste /Lelest3.3.html”>两种对正常序系数</a>的方法。整数序列杂志,第20卷(2017),第17章3.5节。

%HT T.Copand,< HeRF= =“http://TCjp.WordPress .com/2012/11/29/Funigiges Pascal金字塔和WITT和ViasoRo代数/”>无穷小生成器、Pascal金字塔、WITT和Virasoro Algebras </A>

%H.H.,S. Seo,< HeRF= =“http://dx.doi.org/10.1016/j.Ejc.2007 7.122”>贝塞尔数</a>,Eur的逆关系和对数凹性的组合证明。J. Combinat。29(7)(2008)1544-1554。〔3月20日2009〕

%h S. Yang和Z. Qiao,< HeRF= =“HTTP:/JMR.DLUT.EdUnCN/En/CH/Reale/CuraTyPPDF.ASPX”FielyNo=20110406和年份ID=2011和QualthyId=4和Falg=1>贝塞尔数和贝塞尔矩阵</A>,《数学研究与博览会》,2011年7月,第31卷,第4期,第627页-636页。[来自汤姆·科普兰德,12月18日2013 ]

%F数三角形T(n,k)=k!*C(n,k)/((2k- n)!* 2 ^(N-K)。

%f t(n,k)=a00 1498(k,n- k)。-迈克尔索莫斯,10月03日2006

%F E.F.:EXP(y(x+x^ 2/2))。-杰弗里克里特兹,五月08日2012

%F三角形等于矩阵乘积A00 8255*A039 75。同样地,第n行多项式r(n,x)由Type B Dobinski公式r(n,x)=EXP(-x/2)*SuMu{{k>=0 } p(n,2×k+1)*(x/2)^ k/k给出!其中p(n,x)=x*(x-1)**(x n+1)表示落阶乘多项式。参见A11378.-彼得巴拉耶,6月23日2014

%E三角形开始

%E 1;

%E 0, 1;

%E 0, 1, 1;

%E 0, 0, 3,1;

%E 0, 0, 3,6, 1;

%E 0, 0, 0,15, 10, 1;

%E 0, 0, 0、15, 45, 15、1;

%E 0, 0, 0、0, 105, 105、21, 1;

在A26428中定义了函数BELL矩阵。

%p BelMatc(n->IF(n<2,1,0),9);2016,1月27日

%t t[n],k]:= k!*二项式[n,k] /((2 k-n)!* 2 ^(n- k);表[t[n,k],{n,0, 11 },{k,0,n}//平坦

%t(*第二程序:*)

%t行=12;

%t=联接[ { 1, 1 },表[ 0,行] ];

%t t[n],k]:=腹[n,k,t];

%t表[t[n,k],{n,0,行},{k,0,n} / /平坦(*-Jeang-Frang-Oras-Alcopi],6月23日2018,在彼得卢斯尼耶夫*之后)

%O(PARI){t(n,k)=f(2×k<nk k>n,0,n)!/(2×K-N)!/(N-K)!* 2 ^(K-N)}/**迈克尔索莫斯,OCT 03×2006*/

%O(SAGE)α使用[来自A265605]的反相Bell变换

%O MultFase2Y1=lambda n:PRD(k=2×k+ 1(0…n-1))

%O反演Belax矩阵(MulthFask2Y1,9)α,彼得卢斯尼耶夫,12月31日2015

%Y CF.A00 1497、A00 8255、A039 75、A049 403、A0967 13、A1045 56、A111924、A11327、A13077。

%K易,NON,Tabl,改变

%0,9

9月14日,2006岁的A·保罗·巴里亚

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最后修改4月3日18:40 EDT 2020。包含333198个序列。(在OEIS4上运行)