A337027 a(n) = (1/2) * Sum_{k>=0} (2*k + n)^n / 2^k.

1, 3, 24, 293, 4784, 97687, 2393472, 68405073, 2233928448, 82063263371, 3349249267712, 150353137462717, 7362889615257600, 390601858379350815, 22315011551291080704, 1365896953310909493929, 89179296762081886011392, 6186383336743041502051219

Offset

0,2

Links

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

Formula

a(n) = n! * [x^n] exp(n*x) / (2 - exp(2*x)).

a(n) = Sum_{k=0..n} binomial(n,k) * n^k * A216794(n-k).

Mathematica

Table[2^(n - 1) HurwitzLerchPhi[1/2, -n, n/2], {n, 0, 17}]
Table[n! SeriesCoefficient[Exp[n x]/(2 - Exp[2 x]), {x, 0, n}], {n, 0, 17}]

Crossrefs

Cf. A080253, A162314, A216794, A292916.

Sequence in context: A052592 A059381 A301933 * A326001 A365998 A292186

Adjacent sequences: A337024 A337025 A337026 * A337028 A337029 A337030

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 11 2020

Status

approved