A102321 Column 0 of triangular matrix A102320, which satisfies T(n,k) = [T^2](n-1,k) when n>k>=0, with T(n,n) = (2*n+1).

1, 1, 4, 33, 436, 8122, 197920, 6007205, 219413116, 9402081718, 463548752912, 25893783163498, 1618536618626888, 112053082721454708, 8518619080226661504, 705977323976245345133, 63382036275445226941548

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

G.f.: 1 = Sum_{n>=0} a(n)*x^n*prod_{k=0, n} (1-(2k+1)*x) for n>0 with a(0)=1.

Example

G.f.: 1 = (1-x) + 1*x*(1-x)(1-3x) + 4*x^2*(1-x)(1-3x)(1-5x) + ... + a(n)*x^n*(1-x)(1-3x)(1-5x)*..*(1-(2n+1)*x) + ...

Prog

(PARI) {a(n)=local(A=Mat(1), B); for(m=2, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i, j]=2*j-1, if(j==1, B[i, j]=(A^2)[i-1, 1], B[i, j]=(A^2)[i-1, j])); )); A=B); return(A[n+1, 1])}
(PARI) {a(n)=if(n==0, 1, polcoeff(1-sum(k=0, n-1, a(k)*x^k*prod(j=0, k, 1-(2*j+1)*x+x*O(x^n))), n))}

Crossrefs

Cf. A102087, A102323.

Sequence in context: A277184 A192548 A119821 * A268293 A193421 A179421

Adjacent sequences: A102318 A102319 A102320 * A102322 A102323 A102324

Keyword

nonn

Author

Paul D. Hanna, Jan 05 2005

Status

approved