A277464 - OEIS

%I #18 Feb 15 2023 11:08:37

%S 1,1,5,30,281,3400,50557,890120,18101617,417464064,10764826421,

%T 306893014912,9584448407305,325407839778944,11933432488693549,

%U 470087171351873280,19796492491889197025,887518214183286390784,42202928616264032249701,2121583256369642798845952

%N Expansion of e.g.f. cosh(x)/(1 + LambertW(-x)).

%H G. C. Greubel, <a href="/A277464/b277464.txt">Table of n, a(n) for n = 0..385</a>

%F a(n) ~ cosh(exp(-1)) * n^n.

%F a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^(n-2*k) * binomial(n,2*k). -  _Seiichi Manyama_, Feb 15 2023

%t CoefficientList[Series[Cosh[x]/(1+LambertW[-x]), {x, 0, 25}], x] * Range[0, 25]!

%t Table[(1+(-1)^n + Sum[(1+(-1)^(n-k)) * Binomial[n,k] * k^k, {k, 1, n}])/2, {n, 0, 25}]

%o (PARI) x='x+O('x^50); Vec(serlaplace(cosh(x)/(1 + lambertw(-x)))) \\ _G. C. Greubel_, Nov 07 2017

%o (PARI) a(n) = sum(k=0, n\2, (n-2*k)^(n-2*k)*binomial(n, 2*k)); \\ _Seiichi Manyama_, Feb 15 2023

%Y Cf. A000312, A069856, A086331, A277462, A277463.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Oct 16 2016