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A360647 Expansion of Sum_{k>=0} (k^2 * x * (1 + x))^k. 1
1, 1, 17, 761, 67739, 10029956, 2226004406, 691381685259, 286255287677425, 152360721379689043, 101358756787489940837, 82408168580060017122144, 80396790074312939684672316, 92691781529853274368541343021 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=0..floor(n/2)} (n-k)^(2*(n-k)) * binomial(n-k,k).
a(n) ~ n^(2*n). - Vaclav Kotesovec, Feb 16 2023
MATHEMATICA
Flatten[{1, Table[Sum[Binomial[n-k, k] * (n-k)^(2*(n-k)), {k, 0, n/2}], {n, 1, 30}]}] (* Vaclav Kotesovec, Feb 16 2023 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^2*x*(1+x))^k))
(PARI) a(n) = sum(k=0, n\2, (n-k)^(2*(n-k))*binomial(n-k, k));
CROSSREFS
Sequence in context: A283579 A294757 A176233 * A355495 A368492 A012221
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 15 2023
STATUS
approved

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Last modified April 17 13:58 EDT 2024. Contains 371764 sequences. (Running on oeis4.)