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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
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.
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 21 2005
STATUS
approved