A352944 a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^k.

1, 1, 1, 2, 3, 5, 9, 16, 31, 61, 125, 266, 579, 1305, 3009, 7120, 17255, 42697, 108005, 278466, 731883, 1958589, 5331625, 14758720, 41501135, 118507301, 343405709, 1009313322, 3007557523, 9081204849, 27775308049, 86014412384, 269603741111, 855012176081

Offset

0,4

Links

Table of n, a(n) for n=0..33.

Formula

G.f.: Sum_{k>=0} x^k / (1 - k * x^2).

a(n) ~ sqrt(Pi) * (n/LambertW(exp(1)*n))^((n + 1 - n/LambertW(exp(1)*n))/2) / sqrt(1 + LambertW(exp(1)*n)). - Vaclav Kotesovec, Apr 14 2022

Mathematica

Join[{1}, Table[Sum[(n-2k)^k, {k, 0, Floor[n/2]}], {n, 40}]] (* Harvey P. Dale, Dec 12 2022 *)

Prog

(PARI) a(n) = sum(k=0, n\2, (n-2*k)^k);
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-k*x^2)))

Crossrefs

Cf. A026898, A104872, A352946.

Cf. A087811.

Sequence in context: A047061 A136169 A047041 * A154223 A061031 A339512

Adjacent sequences: A352941 A352942 A352943 * A352945 A352946 A352947

Keyword

nonn,easy

Author

Seiichi Manyama, Apr 09 2022

Status

approved