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A347987 a(n) = [x^n] (2*n)! * Sum_{k=0..2*n} binomial(x,k). 8
1, 1, 11, -75, 3969, -140595, 7374191, -435638203, 30421321073, -2409092861175, 214562251828275, -21195275581114635, 2301157855016159905, -272330254968023391035, 34894294917147760652775, -4812715265513253499593675, 710922905477027337578759265, -111981455662673544130741177455 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = A054651(2*n,n) = A190782(2*n,n).
a(n) = [x^(2*n)] ((2*n)!/n!) * (log(1 + x))^n/(1 - x).
a(n) ~ (-1)^n * c * d^n * (n-1)!, where d = 8*w^2/(2*w-1), where w = -LambertW(-1,-exp(-1/2)/2) = 1.7564312086261696769827376166... and c = 0.0754348897003844405252291731755274... - Vaclav Kotesovec, Sep 27 2021
PROG
(PARI) a(n) = (2*n)!*polcoef(sum(k=n, 2*n, binomial(x, k)), n);
CROSSREFS
Sequence in context: A289419 A027226 A300925 * A157232 A305661 A287330
KEYWORD
sign
AUTHOR
Seiichi Manyama, Sep 23 2021
STATUS
approved

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Last modified February 27 15:52 EST 2024. Contains 370377 sequences. (Running on oeis4.)