来自在线整数百科全书的问候语!http://oeis.org/ Search: id:a124322 Showing 1-1 of 1 %I A124322 %S A124322 1,1,1,1,2,3,5,7,3,12,25,15,37,91,60,15,128,329,315,105,457,1415,1533, %T A124322 630,105,1872,6297,7623,4410,945,8169,29431,42150,27405,7875,945, %U A124322 37600,151085,233475,176715,69300,10395,188685,802099,1365243,1199220,533610 %N A124322 Triangle read by rows: T(n,k) is the number of set partitions of {1,2,...,n} (or of any n-set) having k blocks of even size (0<=k<=floor(n/2)). %C A124322 Row n has 1+floor(n/2) terms. 行n的和是贝尔数B(n)=a000 0110(n)。和(k*t(n,k),k=0…楼层(n/2))=a10228 7(n)。t(n,0)=A000 724(n).0%D A124322 L. Comtet,高级组合数学,ReIDL,1974,P 225。行n=0…200,扁平化%F A124322 E.g.f.: exp[sinh(z)+t(cosh(z)-1)]. %e A124322 T(4,1) = 7 because we have 1234, 14|2|3, 1|24|3, 1|2|34, 13|2|4, 1|23|4 and 12|3|4. %e A124322 Triangle starts: %e A124322 1; %e A124322 1; %e A124322 1,1; %e A124322 2,3; %e A124322 5,7,3; %e A124322 12,25,15; %e A124322 37,91,60,15; %p A124322 G:=exp(sinh(z)+t*(cosh(z)-1)): Gser:=simplify(series(G,z=0,16)): for n from 0 to 13 do P[n]:=sort(n!On:对于n从0到13,Doq(COFEF(p[n],t,j),j=0…楼层(n/2));δ屈服序列为三角形%p A124322第二枫程序:(%%A124322与(组合)):%%P A124322B:= PROC(n,i)选项记住;展开(如果n=0, 1,πA124322` IF’(i<1, 0,加法)(多项式(n,ni-*j,i $ j)/j!* COEFF(GSER,Z,(i,2)=0,x^ j,1),j=0…n124322结束:% %p a124322 t=n->(p>SEQ(COEFF(p,x,i),i=0…(p)))(b)p a124322 SEQ(t(n),n=0…15);α-AlOLIS p HeNZZ,MAR 08 2015 2015 % T A124322 NN=10;范围[0,nN]!*%%P A124322B(N-I*J,I-1)*IF(IRM){x,0,nN},{x,y} //Grid(*-Geof Feffy CurrZiz,8月28日2012 *).A000 0110,A10828,A000 724,A124321.K %A124322 NON,TABF %AO A124322,05%,A124322,EMEDER DeutsHig,10月28日2006‰内容在OEIS最终用户许可协议下可用:HTTP:/OEIS.Org/许可证系数列表[EXP[Y(COSH [X] - 1)+SHIH[X] ],