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A347989
a(n) = [x^n] (2*n)! * Sum_{k=0..2*n} binomial(x+k,k).
2
1, 5, 71, 1665, 54649, 2310945, 119753843, 7353403057, 522289211873, 42137920501677, 3807384320667135, 380929847762489025, 41811136672902061321, 4995760464106519955705, 645541681316043216096315, 89705032647088734873129825, 13340173206548155385625683265, 2114001534402053456524492822485
OFFSET
0,2
LINKS
FORMULA
a(n) = (2*n)! * Sum_{k=n..2*n} (2*n+1-k) * |Stirling1(k,n)|/k!.
a(n) = [x^(2*n)] ((2*n)!/n!) * (-log(1 - x))^n/(1 - x)^2.
From Vaclav Kotesovec, Sep 23 2021: (Start)
a(n) = [x^n] Gamma(2*n + x + 2) / Gamma(x + 2).
a(n) ~ c * d^n * (n-1)!, where d = 8*w^2/(2*w-1), w = -LambertW(-1,-exp(-1/2)/2) and c = 1.5967712192197964362930380385801737624829174112909160160618... (End)
PROG
(PARI) a(n) = (2*n)!*polcoef(sum(k=n, 2*n, binomial(x+k, k)), n);
(PARI) a(n) = (2*n)!*sum(k=n, 2*n, (2*n+1-k)*abs(stirling(k, n, 1))/k!);
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 23 2021
STATUS
approved