A343672 - OEIS

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A343672

a(0) = 1; a(n) = 2 * n * a(n-1) + Sum_{k=0..n-1} binomial(n,k) * a(k).

1, 3, 19, 181, 2299, 36501, 695427, 15457709, 392672651, 11221959685, 356339728243, 12446649786429, 474273933636411, 19577992095770837, 870345573347448803, 41455153171478627533, 2106173029315813515883, 113694251997087087941925, 6498401704686168598548435, 392062852538564346207533789

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

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

FORMULA

E.g.f.: 1 / (2 * (1 - x) - exp(x)).

a(n) ~ n! / (2*(1 + LambertW(exp(1)/2)) * (1 - LambertW(exp(1)/2))^(n+1)). - Vaclav Kotesovec, Jun 20 2022

MATHEMATICA

a[0] = 1; a[n_] := a[n] = 2 n a[n - 1] + Sum[Binomial[n, k] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 19}]

nmax = 19; CoefficientList[Series[1/(2 (1 - x) - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!

CROSSREFS