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A360708
Expansion of Sum_{k>=0} (x^2 / (1 - k*x))^k.
4
1, 0, 1, 1, 2, 5, 14, 42, 136, 479, 1825, 7433, 32053, 145608, 695081, 3479117, 18209842, 99373513, 563920590, 3320674902, 20255823092, 127799984935, 832807892861, 5597481205009, 38753768384761, 276057156622776, 2021100095469577, 15193591060371577
OFFSET
0,5
LINKS
FORMULA
a(n) = Sum_{k=1..floor(n/2)} k^(n-2*k) * binomial(n-k-1,k-1) for n > 0.
MATHEMATICA
Join[{1}, Table[Sum[Binomial[n-k-1, k-1] * k^(n-2*k), {k, 0, n/2}], {n, 1, 40}]] (* Vaclav Kotesovec, Feb 20 2023 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (x^2/(1-k*x))^k))
(PARI) a(n) = if(n==0, 1, sum(k=1, n\2, k^(n-2*k)*binomial(n-k-1, k-1)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 17 2023
STATUS
approved