A353013 a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^(n-k).

1, 1, 4, 28, 264, 3207, 47696, 839412, 17061280, 393264145, 10135913792, 288839201432, 9017184333440, 306045200463519, 11220008681600256, 441866073895351128, 18603606156815235584, 833860238440653331505, 39643749441387211150336

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

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

Mathematica

a[0] = 1; a[n_] := Sum[(n - 2*k)^(n - k), {k, 0, Floor[n/2]}]; Array[a, 20, 0] (* Amiram Eldar, Apr 16 2022 *)

Prog

(PARI) a(n) = sum(k=0, n\2, (n-2*k)^(n-k));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k/(1-k*x^2)))

Crossrefs

Cf. A031971, A353014.

Cf. A352981, A352944.

Sequence in context: A292810 A368892 A360727 * A284756 A316144 A138272

Adjacent sequences: A353010 A353011 A353012 * A353014 A353015 A353016

Keyword

nonn,easy

Author

Seiichi Manyama, Apr 16 2022

Status

approved