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128084英镑 |
| 偶数双阶乘q模拟中q系数的三角形,由n^2+1项行读取:T(n,k)=[q^k]Product_{j=1..n}(1-q^(2j))/(1-q)表示n>0,T(0,0)=1。 |
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1, 1, 1, 1, 2, 2, 2, 1, 1, 3, 5, 7, 8, 8, 7, 5, 3, 1, 1, 4, 9, 16, 24, 32, 39, 44, 46, 44, 39, 32, 24, 16, 9, 4, 1, 1, 5, 14, 30, 54, 86, 125, 169, 215, 259, 297, 325, 340, 340, 325, 297, 259, 215, 169, 125, 86, 54, 30, 14, 5, 1, 1, 6, 20, 50, 104, 190, 315, 484, 699, 958, 1255, 1580, 1919, 2254, 2565, 2832, 3037, 3166, 3210, 3166, 3037, 2832, 2565, 2254, 1919, 1580, 1255, 958, 699, 484, 315, 190, 104, 50, 20, 6, 1, 1, 7, 27, 77, 181, 371, 686, 1170, 1869, 2827, 4082, 5662, 7581, 9835, 12399, 15225, 18242, 21358, 24464, 27440, 30162, 32510, 34376, 35672, 36336
(列表;图表;参考;听;历史;文本;内部格式)
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抵消
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0,5
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评论
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行最大值~2^n*n/(sigma*sqrt(2*Pi)),sigma^2=(4*n^3+6*n^2-n)/36=Coxeter群B_n的方差(另见A161858号). -米哈伊尔·盖琴科夫2023年2月8日
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链接
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例子
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[1,2,8,48,384,3840,46080,645120,…,(2n)!!,…]。
三角形开始:
1;
1, 1;
1, 2, 2, 2, 1;
1, 3, 5, 7, 8, 8, 7, 5, 3, 1;
1, 4, 9, 16, 24, 32, 39, 44, 46, 44, 39, 32, 24, 16, 9, 4, 1;
1, 5, 14, 30, 54, 86, 125, 169, 215, 259, 297, 325, 340, 340, 325, 297, 259, 215, 169, 125, 86, 54, 30, 14, 5, 1;
1, 6, 20, 50, 104, 190, 315, 484, 699, 958, 1255, 1580, 1919, 2254, 2565, 2832, 3037, 3166, 3210, 3166, 3037, 2832, 2565, 2254, 1919, 1580, 1255, 958, 699, 484, 315, 190, 104, 50, 20, 6, 1;
1, 7, 27, 77, 181, 371, 686, 1170, 1869, 2827, 4082, 5662, 7581, 9835, 12399, 15225, 18242, 21358, 24464, 27440, 30162, 32510, 34376, 35672, 36336, 36336, ...; ...
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数学
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t[n_,k_]:=如果[k<0|k>n^2,0,如果[n==0,1,系数[级数[积[(1-q^(2*j))/(1-q),{j,1,n}],{q,0,n^2}],q,k]];表[t[n,k],{n,0,6},{k,0,n^2}]//展平(*Jean-François Alcover公司,2013年3月6日,译自巴黎*)
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黄体脂酮素
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(PARI){T(n,k)=如果(k<0|k>n^2,0,如果(n==0,1,polceoff(prod(j=1,n,(1-q^(2*j))/(1-q)),k,q))}
对于(n=0,8,对于(k=0,n^2,打印1(T(n,k),“,”));打印(“”)
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交叉参考
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关键词
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非n,标签
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作者
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状态
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经核准的
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