A343685 a(0) = 1; a(n) = 2 * n * a(n-1) + Sum_{k=0..n-1} binomial(n,k) * (n-k-1)! * a(k).

1, 3, 19, 182, 2328, 37234, 714674, 16004064, 409587144, 11792756640, 377261048592, 13275818803488, 509646721402032, 21195285059025648, 949279217570464944, 45552467588773815744, 2331624264279599225088, 126804353256754734370176, 7301857349340031590836352, 443826900013575494233057536

Offset

0,2

Links

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

Formula

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

a(n) ~ n! / ((2/c + 1 - c) * (1 - c/2)^n), where c = LambertW(2*exp(1)) = 1.3748225281836233816178373171119... - Vaclav Kotesovec, Apr 26 2021

Mathematica

a[0] = 1; a[n_] := a[n] = 2 n a[n - 1] + Sum[Binomial[n, k] (n - k - 1)! a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 19}]
nmax = 19; CoefficientList[Series[1/(1 - 2 x + Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!

Crossrefs

Cf. A007840, A010842, A052820, A343686, A343687.

Sequence in context: A161630 A371320 A121083 * A213533 A203133 A006531

Adjacent sequences: A343682 A343683 A343684 * A343686 A343687 A343688

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 26 2021

Status

approved