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A337027 a(n) = (1/2) * Sum_{k>=0} (2*k + n)^n / 2^k. 0
1, 3, 24, 293, 4784, 97687, 2393472, 68405073, 2233928448, 82063263371, 3349249267712, 150353137462717, 7362889615257600, 390601858379350815, 22315011551291080704, 1365896953310909493929, 89179296762081886011392, 6186383336743041502051219 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
Sequence in context: A052592 A059381 A301933 * A326001 A365998 A292186
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 11 2020
STATUS
approved

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Last modified May 18 02:38 EDT 2024. Contains 372617 sequences. (Running on oeis4.)