A337554 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (5*k-4) * a(n-k).

1, 1, 8, 53, 560, 6961, 105898, 1867393, 37713620, 856269401, 21606253238, 599664843433, 18156702186880, 595557844417441, 21037627605306578, 796218790808110673, 32143778726932363340, 1378765268603813275081, 62619174356163136219918, 3001963660666272082265113

Offset

0,3

Links

Table of n, a(n) for n=0..19.

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

Cf. A000354, A001908, A337552, A337553.

Sequence in context: A252824 A054418 A293115 * A370359 A070928 A180095

Adjacent sequences: A337551 A337552 A337553 * A337555 A337556 A337557

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 31 2020

Status

approved