A353016 a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^(2*k).

1, 1, 1, 2, 5, 11, 33, 108, 357, 1405, 5713, 24670, 117413, 574007, 3004577, 16608120, 95057925, 576245913, 3622049809, 23693870554, 161816447365, 1140392550275, 8351286979745, 63206781102116, 493344133444389, 3980464191557205, 33029872125113937, 282290255465835382

Offset

0,4

Links

Table of n, a(n) for n=0..27.

Formula

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

a(n) = (A062811(n) + 1)/2 for n > 0. - Hugo Pfoertner, Apr 16 2022

Mathematica

a[0] = 1; a[n_] := Sum[(n-2*k)^(2*k), {k, 0, Floor[n/2]}]; Array[a, 30, 0] (* Amiram Eldar, Apr 16 2022 *)

Prog

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

Crossrefs

Cf. A062811, A352082, A352944.

Sequence in context: A379608 A056365 A276548 * A006400 A254342 A080068

Adjacent sequences: A353013 A353014 A353015 * A353017 A353018 A353019

Keyword

nonn,easy

Author

Seiichi Manyama, Apr 16 2022

Status

approved