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A337554
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (5*k-4) * a(n-k).
2
1, 1, 8, 53, 560, 6961, 105898, 1867393, 37713620, 856269401, 21606253238, 599664843433, 18156702186880, 595557844417441, 21037627605306578, 796218790808110673, 32143778726932363340, 1378765268603813275081, 62619174356163136219918, 3001963660666272082265113
OFFSET
0,3
FORMULA
E.g.f.: 1 / (exp(x) * (4 - 5*x) - 3).
a(n) ~ n! * c / (3*(1-c) * (4/5 - c)^(n+1)), where c = -LambertW(-3*exp(-4/5)/5). - Vaclav Kotesovec, Aug 31 2020
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] (5 k - 4) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]
nmax = 19; CoefficientList[Series[1/(Exp[x] (4 - 5 x) - 3), {x, 0, nmax}], x] Range[0, nmax]!
PROG
(PARI) seq(n)={Vec(serlaplace(1 / (exp(x + O(x*x^n)) * (4 - 5*x) - 3)))} \\ Andrew Howroyd, Aug 31 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 31 2020
STATUS
approved