A349556 E.g.f. satisfies: A(x) = 1/(1 - x*A(x))^A(x).

1, 1, 6, 69, 1196, 27900, 820554, 29168048, 1216826120, 58301363808, 3155539049040, 190434409300872, 12679792851087768, 923409652630222680, 73016802381788896344, 6230201355664856039640, 570574779781503603910464, 55826084651771645745562368

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = Sum_{k=0..n} (n+k+1)^(k-1) * |Stirling1(n,k)|.

a(n) ~ s^2 * sqrt((1 - r*s) / (1 + r*s*(s-1) * (2 - r*s))) * n^(n-1) / (exp(n) * r^(n - 1/2)), where r = 0.1591040778917510493879632960549533860431737829556... and s = 1.588466710327904339474066925768589168215650366378... are real roots of the system of equations 1/s = (1 - r*s)^s, r*s/(1 - r*s) - log(1 - r*s) = 1/s. - Vaclav Kotesovec, Nov 22 2021

Mathematica

a[n_] := Sum[(n + k + 1)^(k - 1) * Abs[StirlingS1[n, k]], {k, 0, n}]; Array[a, 18, 0] (* Amiram Eldar, Nov 22 2021 *)

Prog

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

Crossrefs

Cf. A052813, A162655, A349559.

Sequence in context: A177751 A338176 A235327 * A364982 A098639 A305110

Adjacent sequences: A349553 A349554 A349555 * A349557 A349558 A349559

Keyword

nonn

Author

Seiichi Manyama, Nov 21 2021

Status

approved