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A346394
Expansion of e.g.f. -log(1 - x) * exp(2*x).
4
0, 1, 5, 20, 78, 324, 1520, 8336, 53872, 405600, 3492416, 33798016, 362543104, 4264455168, 54540715008, 753246711808, 11168972683264, 176937613586432, 2982069587042304, 53271637651996672, 1005385746384846848, 19987620914387812352, 417489079682758213632
OFFSET
0,3
LINKS
FORMULA
a(n) = n! * Sum_{k=0..n-1} 2^k / ((n-k) * k!).
a(n) = Sum_{k=0..n} binomial(n,k) * A002104(k).
a(n) ~ exp(2) * (n-1)!. - Vaclav Kotesovec, Aug 09 2021
a(0) = 0, a(1) = 1, a(n) = (n+1) * a(n-1) - 2 * (n-1) * a(n-2) + 2^(n-1). - Seiichi Manyama, May 27 2022
MATHEMATICA
nmax = 22; CoefficientList[Series[-Log[1 - x] Exp[2 x], {x, 0, nmax}], x] Range[0, nmax]!
Table[n! Sum[2^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+1)*v[i]-2*(i-1)*v[i-1]+2^(i-1)); v; \\ Seiichi Manyama, May 27 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 15 2021
STATUS
approved