A337058 E.g.f.: 1 / (2 + x^2/2 - exp(x)).

1, 1, 2, 7, 33, 191, 1323, 10711, 99151, 1032385, 11943003, 151979213, 2109829857, 31730171539, 513903517585, 8917723105003, 165065061436755, 3246274767649637, 67598797715175999, 1485845872704318265, 34378343609138619685, 835190283258080561671

Offset: 0

Author

Ilya Gutkovskiy, Aug 13 2020

Keywords

• nonn

Crossrefs

Cf. A000670, A032032, A097514, A102233, A337059.

Programs

Mathematica

nmax = 21; CoefficientList[Series[1/(2 + x^2/2 - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = n a[n - 1] + Sum[Binomial[n, k] a[n - k], {k, 3, n}]; Table[a[n], {n, 0, 21}]

Formula

a(0) = 1; a(n) = n * a(n-1) + Sum_{k=3..n} binomial(n,k) * a(n-k).