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A102917 Column 0 of triangle A102916. 3
1, 1, 1, 3, 7, 36, 139, 1036, 5711, 56355, 408354, 5045370, 45605881, 679409158, 7390305396, 129195427716, 1647470410551, 33114233390505, 485292763088275, 11038606786054201, 183049273155939442, 4652371578279864792 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 20 09:35 EDT 2019. Contains 321345 sequences. (Running on oeis4.)