A346398 Expansion of e.g.f. -log(1 - x) * exp(-3*x).

0, 1, -5, 20, -72, 249, -825, 2736, -8568, 29385, -74709, 417636, 698544, 21853233, 244181223, 3608612208, 54277152624, 878859416817, 15072037479099, 273539358115092, 5235734703888648, 105419854939796937, 2227408664800976487, 49278475088626210704, 1139260699549648412856

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..451

Formula

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

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

a(n) ~ exp(-3) * (n-1)!. - Vaclav Kotesovec, Jun 08 2022

Mathematica

nmax = 24; CoefficientList[Series[-Log[1 - x] Exp[-3 x], {x, 0, nmax}], x] Range[0, nmax]!
Table[n! Sum[(-3)^k/((n - k) k!), {k, 0, n - 1}], {n, 0, 24}]

Prog

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

Crossrefs

Cf. A002741, A010843, A346397.

Sequence in context: A269914 A066822 A137212 * A270080 A271136 A118049

Adjacent sequences: A346395 A346396 A346397 * A346399 A346400 A346401

Keyword

sign

Author

Ilya Gutkovskiy, Jul 15 2021

Status

approved