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 A335529 a(n) = n! * [x^n] (1 - (n-1)*log(1 + x))/(1 - n*log(1 + x)). 1
 1, 1, 3, 38, 1042, 49774, 3661128, 383653080, 54275300112, 9964363066848, 2303245150868640, 654457584668128416, 224205104879416320768, 91129285853151907958544, 43356207229026959513863680, 23868203329368882698589532800, 15053662436260897659550535387136 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA a(n) = A317172(n)/n = Sum_{k=0..n} k!*n^(k-1)*Stirling1(n,k) for n > 1. a(n) ~ sqrt(2*Pi) * n^(2*n - 1/2) / exp(n + 1/2). - Vaclav Kotesovec, Jun 12 2020 MATHEMATICA a[0] = 1; a[n_] := Sum[k! * n^(k - 1) * StirlingS1[n, k], {k, 0, n}]; Array[a, 17, 0] (* Amiram Eldar, Jun 12 2020 *) PROG (PARI) {a(n) = if(n==0, 1, sum(k=0, n, k!*n^(k-1)*stirling(n, k, 1)))} CROSSREFS Main diagonal of A334369. Cf. A317172, A321189. Sequence in context: A300627 A158119 A263332 * A062155 A278927 A099022 Adjacent sequences:  A335526 A335527 A335528 * A335530 A335531 A335533 KEYWORD nonn AUTHOR Seiichi Manyama, Jun 12 2020 STATUS approved

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Last modified September 29 05:48 EDT 2020. Contains 337425 sequences. (Running on oeis4.)