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A102918 Column 1 of triangle A102916. 1
0, 2, 4, 8, 40, 152, 1128, 6200, 61120, 442552, 5466320, 49399320, 735847800, 8003532512, 139910204080, 1784040237288, 35858685086352, 525504809786112, 11953187179149408, 198213959637435608, 5037776918810353960 (list; graph; refs; listen; history; text; internal format)
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 * A018395 A136538 A018403

Adjacent sequences:  A102915 A102916 A102917 * A102919 A102920 A102921

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 21 2005

STATUS

approved

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Last modified March 25 22:28 EDT 2019. Contains 321477 sequences. (Running on oeis4.)