A102918 Column 1 of triangle A102916.

0, 2, 4, 8, 40, 152, 1128, 6200, 61120, 442552, 5466320, 49399320, 735847800, 8003532512, 139910204080, 1784040237288, 35858685086352, 525504809786112, 11953187179149408, 198213959637435608, 5037776918810353960

Offset

0,2

Comments

Also equals the interleaving of A102099 with A102922, which equal column 1 of triangle A102098 and its matrix square (A102920), respectively.

Links

Table of n, a(n) for n=0..20.

Formula

G.f.: 2 = Sum_{n>=0}(a(2*n+1)+a(2*n+2)*x)*x^(2*n)*Product_{k=2..n+2}(1-k*x) where a(2*n+1)=A102099(n+1) and a(2*n+2)=A102922(n+1) with a(0)=0.

Example

2 = 2*(1-2x) + 4*x*(1-2x) + 8*x^2*(1-2x)(1-3x) + 40*x^3*(1-2x)(1-3x)
+ 152*x^4*(1-2x)(1-3x)(1-4x) + 1128*x^5*(1-2x)(1-3x)(1-4x)
+ 6200*x^6*(1-2x)(1-3x)(1-4x)(1-5x) + 61120*x^7*(1-2x)(1-3x)(1-4x)(1-5x) +...
+ A102099(n+1)*x^(2n)*(1-2x)(1-3x)*..*(1-(n+2)x)
+ A102922(n+1)*x^(2n+1)*(1-x)(1-2x)*..*(1-(n+2)x) + ...

Prog

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

Crossrefs

Cf. A102916, A102099, A102922, A102098, A102920.

Sequence in context: A259120 A319595 A285632 * A326951 A018395 A136538

Adjacent sequences: A102915 A102916 A102917 * A102919 A102920 A102921

Keyword

nonn

Author

Paul D. Hanna, Jan 21 2005

Status

approved