A389866 - OEIS

A389866

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

1, 2, 15, 193, 3441, 79261, 2253493, 76467371, 3020431473, 136258479577, 6916286910501, 390287871050815, 24245250206489689, 1644505983024192341, 120948003064125902421, 9588198232337741477011, 815113777054199768402529, 73976301828137552007193393, 7139090736894012540234700357

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..300

FORMULA

E.g.f.: exp( -LambertW(-x/(1-x)^4) )/(1-x).

a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(n+3*k,n-k)/k!.

MATHEMATICA

Table[n!*Sum[(k+1)^(k-1)*Binomial[n+3*k, n-k]/k!, {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Nov 05 2025 *)

PROG

(PARI) a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(n+3*k, n-k)/k!);