A346396 Expansion of e.g.f. -log(1 - x) * exp(4*x).

0, 1, 9, 62, 390, 2384, 14680, 93680, 635824, 4697664, 38442112, 351331584, 3582715136, 40476303360, 501863078912, 6767130867712, 98464775493632, 1536203429306368, 25564684461735936, 451816479967608832, 8448863295040978944, 166627401783086415872, 3455980532191764676608

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..450

Formula

a(n) = n! * Sum_{k=0..n-1} 4^k / ((n-k) * k!).

a(n) ~ exp(4) * (n-1)!. - Vaclav Kotesovec, Aug 09 2021

a(0) = 0, a(1) = 1, a(n) = (n+3) * a(n-1) - 4 * (n-1) * a(n-2) + 4^(n-1). - Seiichi Manyama, May 27 2022

Mathematica

nmax = 22; CoefficientList[Series[-Log[1 - x] Exp[4 x], {x, 0, nmax}], x] Range[0, nmax]!
Table[n! Sum[4^k/((n - k) k!), {k, 0, n - 1}], {n, 0, 22}]

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=0; v[2]=1; for(i=2, n, v[i+1]=(i+3)*v[i]-4*(i-1)*v[i-1]+4^(i-1)); v; \\ Seiichi Manyama, May 27 2022

Crossrefs

Cf. A002104, A053487, A346394, A346395.

Sequence in context: A027234 A081574 A084151 * A240391 A229701 A341627

Adjacent sequences: A346393 A346394 A346395 * A346397 A346398 A346399

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 15 2021

Status

approved