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 A351280 a(n) = Sum_{k=0..n} k! * k^k * Stirling1(n,k). 4
 1, 1, 7, 140, 5254, 318854, 28455182, 3506576856, 570360248856, 118356589567440, 30512901324706608, 9566812017770347152, 3584662956711860108352, 1581905384865801328253712, 812047187127758913474118032, 479763784808095613489811245568 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..15. FORMULA E.g.f.: Sum_{k>=0} (k * log(1+x))^k. a(n) ~ exp(-exp(-1)/2) * n! * n^n. - Vaclav Kotesovec, Feb 06 2022 MATHEMATICA a[0] = 1; a[n_] := Sum[k! * k^k * StirlingS1[n, k], {k, 1, n}]; Array[a, 16, 0] (* Amiram Eldar, Feb 06 2022 *) PROG (PARI) a(n) = sum(k=0, n, k!*k^k*stirling(n, k, 1)); (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*log(1+x))^k))) CROSSREFS Cf. A006252, A305819, A320083, A350721, A350725, A351281. Sequence in context: A297650 A085708 A054606 * A306628 A302912 A191956 Adjacent sequences: A351277 A351278 A351279 * A351281 A351282 A351283 KEYWORD nonn AUTHOR Seiichi Manyama, Feb 06 2022 STATUS approved

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Last modified July 14 19:43 EDT 2024. Contains 374323 sequences. (Running on oeis4.)