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

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

Cf. A000670, A005493, A006155, A032032, A343673, A343674.

Sequence in context: A304578 A306576 A303064 * A161630 A371320 A121083

Adjacent sequences: A343669 A343670 A343671 * A343673 A343674 A343675

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 25 2021

Status

approved