OFFSET
0,3
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 05 2005
STATUS
approved