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 A360611 Expansion of Sum_{k>=0} (k * x * (1 + x))^k. 7
 1, 1, 5, 35, 341, 4230, 63844, 1135753, 23273363, 539881365, 13986073419, 400227436252, 12538263892232, 426810214125441, 15687071552060221, 619144491880324087, 26117514728711229877, 1172635546310430028562, 55833864788507320490268 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Winston de Greef, Table of n, a(n) for n = 0..385 FORMULA a(n) = Sum_{k=0..floor(n/2)} (n-k)^(n-k) * binomial(n-k,k). a(n) ~ exp(exp(-1)) * n^n. - Vaclav Kotesovec, Feb 14 2023 MATHEMATICA Flatten[{1, Table[Sum[Binomial[n-k, k] * (n-k)^(n-k), {k, 0, n/2}], {n, 1, 20}]}] (* Vaclav Kotesovec, Feb 14 2023 *) PROG (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x*(1+x))^k)) (PARI) a(n) = sum(k=0, n\2, (n-k)^(n-k)*binomial(n-k, k)); CROSSREFS Cf. A355494, A360592. Sequence in context: A262248 A346666 A369724 * A201367 A233860 A258902 Adjacent sequences: A360608 A360609 A360610 * A360612 A360613 A360614 KEYWORD nonn AUTHOR Seiichi Manyama, Feb 14 2023 STATUS approved

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Last modified August 14 07:07 EDT 2024. Contains 375146 sequences. (Running on oeis4.)