A380016 - OEIS

%I #7 Jan 09 2025 08:00:45

%S 1,2,13,161,2833,64841,1827685,61192181,2372620801,104549934977,

%T 5160225776101,281994042839477,16902276273364465,1102519010117525105,

%U 77749077431938305541,5894145002422856684501,478015727336387513545345,41295912476641866286397825,3786025873450493919700627525

%N Expansion of e.g.f. 1/(exp(-3*x) - 3*x)^(1/3).

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

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

%Y Cf. A072597, A380014, A380018.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 09 2025