|
|
A353016
|
|
a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^(2*k).
|
|
2
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
LINKS
|
|
|
FORMULA
|
G.f.: Sum_{k>=0} x^k / (1 - (k * x)^2).
|
|
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
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|