A102917 Column 0 of triangle A102916.

1, 1, 1, 3, 7, 36, 139, 1036, 5711, 56355, 408354, 5045370, 45605881, 679409158, 7390305396, 129195427716, 1647470410551, 33114233390505, 485292763088275, 11038606786054201, 183049273155939442, 4652371578279864792

Offset

0,4

Comments

Also equals the interleaving of A082162 with A102921, which equal column 0 of triangle A102098 and its matrix square (A102920), respectively.

Links

Table of n, a(n) for n=0..21.

Formula

G.f.: 1 = Sum_{n>=0}(a(2*n)+a(2*n+1)*x)*x^(2*n)*Product_{k=1..n+1}(1-k*x) where a(2*n)=A082162(n) and a(2*n+1)=A102921(n).

Example

1 = 1*(1-x) + 1*x*(1-x) + 1*x^2*(1-x)(1-2x) + 3*x^3*(1-x)(1-2x)
+ 7*x^4*(1-x)(1-2x)(1-3x) + 36*x^5*(1-x)(1-2x)(1-3x)
+ 139*x^6*(1-x)(1-2x)(1-3x)(1-4x) + 1036*x^7*(1-x)(1-2x)(1-3x)(1-4x) + ...
+ A082162(n)*x^(2n)*(1-x)(1-2x)*..*(1-(n+1)x)
+ A102921(n)*x^(2n+1)*(1-x)(1-2x)*..*(1-(n+1)x) + ...

Prog

(PARI) {a(n)=if(n==0, 1, polcoeff(1-sum(k=0, n-1, a(k)*x^k*prod(j=1, k\2+1, 1-j*x+x*O(x^n))), n))}

Crossrefs

Cf. A102916, A082162, A102921, A102098, A102920.

Sequence in context: A108505 A047158 A221511 * A156465 A049366 A081010

Adjacent sequences: A102914 A102915 A102916 * A102918 A102919 A102920

Keyword

nonn

Author

Paul D. Hanna, Jan 21 2005

Status

approved