A367846 Expansion of e.g.f. 1/(1 - x + log(1 - 3*x)).

1, 4, 41, 654, 14028, 377112, 12177126, 458916588, 19769059944, 958125646080, 51597765220608, 3056601306206016, 197532472461453072, 13829353660386169344, 1042679226974498229456, 84229294995413626072608, 7257792124889497549663488

Offset

0,2

Links

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

Formula

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

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*v[i]+sum(j=1, i, 3^j*(j-1)!*binomial(i, j)*v[i-j+1])); v;

Crossrefs

Cf. A052820, A367845, A367847.

Cf. A367836.

Sequence in context: A230251 A001908 A367836 * A270703 A363302 A361182

Adjacent sequences: A367843 A367844 A367845 * A367847 A367848 A367849

Keyword

nonn

Author

Seiichi Manyama, Dec 02 2023

Status

approved