%I #7 May 07 2018 22:43:21

%S 1,1,4,39,648,15465,483240,18685905,861282832,46085893011,

%T 2807152825020,191731595897600,14510053796849640,1205013817282706730,

%U 108941005329522201360,10650027832902977866245,1119401271751383414197280,125879457463215695125460535

%N Column 1 of triangle A132610.

%C 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.

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

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

%o (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]}

%o for(n=0,25,print1(a(n),", "))

%o (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]}

%o for(n=0,25,print1(a(n),", "))

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

%Y Cf. A304192.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Aug 23 2007