A355766 E.g.f. satisfies A(x) = 1/(1 - x*A(x))^(A(x)^2).

1, 1, 8, 126, 3028, 98540, 4056948, 202301456, 11855415920, 798682318848, 60823290655680, 5167260183157248, 484519323081722784, 49705696509114472320, 5537956421036240838336, 665926312161296782156800, 85960998514145805006711552

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..328

Formula

a(n) = Sum_{k=0..n} (n+2*k+1)^(k-1) * |Stirling1(n,k)|.

a(n) ~ s^(5/2) * n^(n-1) * sqrt((1 - r*s)/(2 - 4*r*s + 2*r^2*s^2 + 3*r*s^3 - 2*r^2*s^4)) / (exp(n) * r^(n - 1/2)), where r = 0.11275303067590951818975824... and s = 1.382171434168172073998532... are real roots of the system of equations (1 - r*s)^(s^2) = 1/s, r*s/(1 - r*s) = 1/s^2 + 2*log(1 - r*s). - Vaclav Kotesovec, Jul 21 2022

Mathematica

Table[Sum[(n + 2*k + 1)^(k - 1)* Abs[StirlingS1[n, k]], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 21 2022 *)

Prog

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

Crossrefs

Cf. A001761, A349556.

Sequence in context: A360852 A262732 A220728 * A029472 A001081 A371368

Adjacent sequences: A355763 A355764 A355765 * A355767 A355768 A355769

Keyword

nonn

Author

Seiichi Manyama, Jul 16 2022

Status

approved