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A360782
Expansion of Sum_{k>=0} x^k / (1 - k*x^2)^(k+1).
5
1, 1, 1, 3, 7, 16, 45, 125, 363, 1127, 3561, 11696, 39727, 138113, 494213, 1811075, 6784115, 25985928, 101520833, 404305549, 1640002039, 6767576175, 28395916893, 121048681024, 523902418555, 2300906314849, 10248029334297, 46266088140291
OFFSET
0,4
FORMULA
a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^k * binomial(n-k,k).
MATHEMATICA
Join[{1}, Table[Sum[Binomial[n-k, k] * (n-2*k)^k, {k, 0, n/2}], {n, 1, 30}]] (* Vaclav Kotesovec, Feb 21 2023 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-k*x^2)^(k+1)))
(PARI) a(n) = sum(k=0, n\2, (n-2*k)^k*binomial(n-k, k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Feb 20 2023
STATUS
approved