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A268149 A double binomial sum involving absolute values. 2
0, 24, 1120, 33264, 823680, 18475600, 389398464, 7862853600, 153876579840, 2940343837200, 55138611528000, 1018383898440480, 18574619721465600, 335240928272918304, 5996573430996184960, 106438123408375281600, 1876607120325212706816, 32891715945378106711440 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A fast algorithm follows from Theorem 1 of Brent et al. article.

LINKS

Table of n, a(n) for n=0..17.

Richard P. Brent, Hideyuki Ohtsuka, Judy-anne H. Osborn, Helmut Prodinger, Some binomial sums involving absolute values, arXiv:1411.1477v2 [math.CO], 2016.

FORMULA

a(n) = Sum_{k=-n..n} (Sum_{l=-n..n} binomial(2*n, n+k)*binomial(2*n, n+l)*abs(k-l)^3).

PROG

(PARI) a(n) = sum(k=-n, n, sum(l=-n, n, binomial(2*n, n+k)*binomial(2*n, n+l)*abs(k-l)^3));

CROSSREFS

Cf. A000984, A002894, A166337, A268147.

Sequence in context: A046906 A130552 A160260 * A114051 A269092 A010562

Adjacent sequences: A268146 A268147 A268148 * A268150 A268151 A268152

KEYWORD

easy,nonn

AUTHOR

Richard P. Brent, Jan 27 2016

STATUS

approved

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Last modified December 8 01:12 EST 2022. Contains 358672 sequences. (Running on oeis4.)