A370922 E.g.f. satisfies A(x) = log(1 + x/(1 - A(x)))/(1 - A(x)).

0, 1, 3, 29, 444, 9454, 257822, 8576504, 336770592, 15246592440, 781883091672, 44797478362680, 2836034500712256, 196601715537070752, 14811696896760459264, 1205008924460733794688, 105284627507520312994560, 9832559605580777568425856

Offset

0,3

Links

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

Index entries for reversions of series

Formula

a(n) = Sum_{k=1..n} (n+2*k-2)!/(n+k-1)! * Stirling1(n,k).

E.g.f.: Series_Reversion( (1 - x) * (exp(x * (1 - x)) - 1) ). - Seiichi Manyama, Sep 09 2024

a(n) ~ s^n * (2*s-3)^n * n^(n-1) / (sqrt(-3 + s + 8*s^2 - 4*s^3) * (1-s)^(2*n-1) * (2*s-1)^(n - 1/2) * exp(n)), where s = 0.34542229482270921728057471620674895969... is the root of the equation log((3-2*s)*s) = s*(s-1). - Vaclav Kotesovec, Jan 23 2026

Mathematica

Table[Sum[(n + 2*k - 2)!/(n + k - 1)!*StirlingS1[n, k], {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jan 23 2026 *)

Prog

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

Crossrefs

Cf. A371326, A371342.

Sequence in context: A335867 A371652 A302923 * A366005 A376038 A326433

Adjacent sequences: A370919 A370920 A370921 * A370923 A370924 A370925

Keyword

nonn

Author

Seiichi Manyama, Mar 19 2024

Status

approved