A367424 Expansion of e.g.f. 1 / (1 + log(1 - 3*x))^(1/3).

1, 1, 7, 82, 1342, 28204, 724276, 21988000, 770703496, 30639393640, 1362480890104, 67018512565168, 3613262889736144, 211897666186184224, 13429569671442331936, 914731985485067825152, 66638964749234715026560, 5170503246184584686976640

Offset

0,3

Links

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

Formula

a(n) = Sum_{k=0..n} 3^(n-k) * (Product_{j=0..k-1} (3*j+1)) * |Stirling1(n,k)|.

a(0) = 1; a(n) = Sum_{k=1..n} 3^k * (1 - 2/3 * k/n) * (k-1)! * binomial(n,k) * a(n-k).

Prog

(PARI) a(n) = sum(k=0, n, 3^(n-k)*prod(j=0, k-1, 3*j+1)*abs(stirling(n, k, 1)));

Crossrefs

Cf. A352070, A352118.

Sequence in context: A361714 A191804 A243672 * A268653 A364939 A360473

Adjacent sequences: A367421 A367422 A367423 * A367425 A367426 A367427

Keyword

nonn

Author

Seiichi Manyama, Nov 18 2023

Status

approved