A132612 Column 1 of triangle A132610.

1, 1, 4, 39, 648, 15465, 483240, 18685905, 861282832, 46085893011, 2807152825020, 191731595897600, 14510053796849640, 1205013817282706730, 108941005329522201360, 10650027832902977866245, 1119401271751383414197280, 125879457463215695125460535

Offset: 0

Author

Paul D. Hanna, Aug 23 2007

Keywords

• nonn

Comments

Triangle T=A132610 is generated by even matrix powers of itself such that row n+1 of T = row n of T^(2n) with appended '1' for n>=0 with T(0,0)=1.

Crossrefs

Cf. A132610 (triangle); other columns: A132611, A132613; A132614.

Cf. A304192.

Programs

PARI

{a(n)=local(A=vector(n+2), p); A[1]=1; for(j=1, n-1, p=n^2-(n-j)^2; A=Vec((Polrev(A)+x*O(x^p))/(1-x))); A=Vec((Polrev(A)+x*O(x^p))/(1-x)); A[p+1]}
for(n=0,25,print1(a(n),", "))

PARI

{a(n)=local(A=[1]);for(i=1,n,A=Vec(Ser(A)/(1-x)^(2*(#A)-1));A=concat(A,A[#A]));A[#A]}
for(n=0,25,print1(a(n),", "))

Formula

a(n) is divisible by n for n>0; a(n)/n = A132614(n).

a(n) = [x^(n-1)] (1+x)^(n*(n+1)) / F(x) for n>0, where F(x) is the g.f. of A304192.