A376035 E.g.f. satisfies A(x) = exp(x / (1 - A(x))^3) - 1.

0, 1, 7, 118, 3205, 120466, 5790619, 339216046, 23443311049, 1867308836986, 168435092561671, 16971155810393302, 1889194092179682061, 230257485553145337106, 30496977601634473249363, 4361533380688447142658046, 669865656003334085318195089

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Index entries for reversions of series

Formula

E.g.f.: Series_Reversion( (1 - x)^3 * log(1+x) ).

a(n) = Sum_{k=1..n} (3*n+k-2)!/(3*n-1)! * Stirling2(n,k).

a(n) ~ 3^(4*n-2) * LambertW(2*exp(1/3)/3)^(3*n-1) * n^(n-1) / (sqrt(1 + LambertW(2*exp(1/3)/3)) * exp(n) * 2^(3*n-1) * (3*LambertW(2*exp(1/3)/3) - 1)^(4*n-1)). - Vaclav Kotesovec, Sep 10 2024

Mathematica

Table[Sum[(3*n+k-2)!/(3*n-1)! * StirlingS2[n, k], {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Sep 10 2024 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(serreverse((1-x)^3*log(1+x)))))
(PARI) a(n) = sum(k=1, n, (3*n+k-2)!/(3*n-1)!*stirling(n, k, 2));

Crossrefs

Cf. A274265, A376034, A376036.

Cf. A052892, A371371.

Sequence in context: A097202 A163202 A213112 * A266482 A368631 A076283

Adjacent sequences: A376032 A376033 A376034 * A376036 A376037 A376038

Keyword

nonn

Author

Seiichi Manyama, Sep 07 2024

Status

approved