A124995 - OEIS

A124995

a(n) is the constant term in expansion of Product_{ k = 1..n } (x^k + 1/x^k)^3.

1, 0, 0, 62, 332, 0, 0, 80006, 531524, 0, 0, 173607568, 1226700784, 0, 0, 455805857978, 3321800235936, 0, 0, 1325490660318216, 9841000101286172, 0, 0, 4108826483323392880, 30886378286619335592, 0, 0, 13306426381421174346512, 100916492010297213463566

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OFFSET

0,4

COMMENTS

From Robert Israel, Nov 09 2017: (Start)

a(n) is the coefficient of x^(3*n*(n+1)/2) in Product_{k=0..n} (x^(2*k)+1)^3.

a(n) = 0 if n == 1 or 2 (mod 4). (End)

LINKS

Ray Chandler, Table of n, a(n) for n = 0..1114 (terms < 10^1000)

Ovidiu Bagdasar and Dorin Andrica, New results and conjectures on 2-partitions of multisets, 2017 7th International Conference on Modeling, Simulation, and Applied Optimization (ICMSAO).

MAPLE

seq(coeff(mul(x^k+1/x^k, k=1..n)^3, x, 0), n=0..50); # Robert Israel, Nov 09 2017

PROG

(PARI) a(n) = polcoef(prod(k=1, n, (x^k + 1/x^k)^3), 0); \\ Michel Marcus, Jan 07 2021

CROSSREFS

For constant term in expansion of Product_{ k = 1..n } (x^k + 1/x^k)^q for other values of q see A063865, A047653, A124996.

Sequence in context: A100160 A223072 A010746 * A020191 A212834 A202959

Adjacent sequences: A124992 A124993 A124994 * A124996 A124997 A124998

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jul 12 2008

STATUS

approved