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A307946 Coefficient of x^n in 1/(n+1) * (1 - n*x - n*x^2)^(n+1). 2
1, -1, 2, 0, -96, 1875, -32184, 554631, -9773056, 172718325, -2874200000, 35973317666, 218394869760, -46968959184459, 2890848443624064, -147665402789062500, 7121567693920010240, -337669517265832692843, 15985827659730523364352, -759295252512454596032456 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also coefficient of x^n in the expansion of 2/(1 + n*x + sqrt(1 + 2*n*x + n*(n+4)*x^2)).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..386

FORMULA

a(n) = Sum_{k=0..floor(n/2)} (-n)^(n-k) * binomial(n,k) * binomial(n-k,k)/(k+1) = Sum_{k=0..floor(n/2)} (-n)^(n-k) * binomial(n,2*k) * A000108(k).

PROG

(PARI) {a(n) = polcoef((1-n*x-n*x^2)^(n+1)/(n+1), n)}

(PARI) {a(n) = sum(k=0, n\2, (-n)^(n-k)*binomial(n, k)*binomial(n-k, k)/(k+1))}

(PARI) {a(n) = sum(k=0, n\2, (-n)^(n-k)*binomial(n, 2*k)*binomial(2*k, k)/(k+1))}

CROSSREFS

Cf. A000108, A292716, A307911.

Sequence in context: A009740 A132860 A156485 * A009270 A033838 A181373

Adjacent sequences:  A307943 A307944 A307945 * A307947 A307948 A307949

KEYWORD

sign

AUTHOR

Seiichi Manyama, May 07 2019

STATUS

approved

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Last modified November 17 18:24 EST 2019. Contains 329241 sequences. (Running on oeis4.)