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A346395
Expanison of e.g.f. -log(1 - x) * exp(3*x).
4
0, 1, 7, 38, 192, 969, 5115, 29322, 187992, 1370745, 11392839, 107043606, 1122823944, 12989320785, 164040593067, 2243143392138, 32994768719376, 519229765892241, 8701862242296807, 154700700117472422, 2907409255935736752, 57588370882960384377, 1198954118077558162875
OFFSET
0,3
LINKS
FORMULA
a(n) = n! * Sum_{k=0..n-1} 3^k / ((n-k) * k!).
a(n) ~ exp(3) * (n-1)!. - Vaclav Kotesovec, Aug 09 2021
a(0) = 0, a(1) = 1, a(n) = (n+2) * a(n-1) - 3 * (n-1) * a(n-2) + 3^(n-1). - Seiichi Manyama, May 27 2022
MATHEMATICA
nmax = 22; 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, 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+2)*v[i]-3*(i-1)*v[i-1]+3^(i-1)); v; \\ Seiichi Manyama, May 27 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 15 2021
STATUS
approved