A349588 E.g.f. satisfies: A(x) * log(A(x)) = exp(x*A(x)) - 1.

1, 1, 2, 8, 47, 367, 3592, 42317, 583522, 9223872, 164482761, 3267077365, 71540314562, 1712334954865, 44479256704898, 1246241906483516, 37465750470667023, 1202986323660907447, 41089436549405467096, 1487622596267089224901, 56907111260864275384346

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..403

Formula

a(n) = Sum_{k=0..n} (n-k+1)^(k-1) * Stirling2(n,k).

a(n) ~ s * n^(n-1) / (sqrt(r*s - 1/(1 + log(s))) * exp(n) * r^n), where r = 0.4858893246242883887847088396703818017675758048583... and s = 3.016426175038226058288579473351450432292607021364... are roots of the system of equations exp(r*s) = 1 + s*log(s), exp(r*s)*r = 1 + log(s). - Vaclav Kotesovec, Nov 25 2021

Mathematica

a[n_] := Sum[(n - k + 1)^(k - 1)*StirlingS2[n, k], {k, 0, n}]; Array[a, 21, 0] (* Amiram Eldar, Nov 23 2021 *)

Prog

(PARI) a(n) = sum(k=0, n, (n-k+1)^(k-1)*stirling(n, k, 2));

Crossrefs

Cf. A141209, A349587, A349589.

Cf. A349557.

Sequence in context: A145846 A317366 A009566 * A259905 A329096 A233337

Adjacent sequences: A349585 A349586 A349587 * A349589 A349590 A349591

Keyword

nonn

Author

Seiichi Manyama, Nov 22 2021

Status

approved