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A352985
a(n) = Sum_{k=0..floor(n/2)} k^(2*(n-2*k)).
0
1, 0, 1, 1, 2, 5, 18, 74, 339, 1770, 10915, 79555, 663140, 6109351, 61264436, 669862580, 8044351557, 106331744724, 1536980041573, 24028469781765, 402558463751974, 7195932984364585, 137204787854813174, 2792969599543659326, 60668198155262809815
OFFSET
0,5
FORMULA
G.f.: Sum_{k>=0} x^(2 * k) / (1 - k^2 * x).
a(n) ~ sqrt(Pi/2) * (n/(2*LambertW(exp(1)*n/2)))^(2*n + 1/2 - 2*n/LambertW(exp(1)*n/2)) / sqrt(1 + LambertW(exp(1)*n/2)). - Vaclav Kotesovec, Apr 14 2022
MATHEMATICA
a[0] = 1; a[n_] := Sum[k^(2*(n - 2*k)), {k, 0, Floor[n/2]}]; Array[a, 25, 0] (* Amiram Eldar, Apr 13 2022 *)
PROG
(PARI) a(n) = sum(k=0, n\2, k^(2*(n-2*k)));
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^(2*k)/(1-k^2*x)))
CROSSREFS
Sequence in context: A162543 A039744 A344262 * A319121 A289655 A189281
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Apr 13 2022
STATUS
approved