A337059 E.g.f.: 1 / (2 + x^3/6 - exp(x)).

1, 1, 3, 12, 67, 461, 3823, 36933, 407963, 5068909, 69982083, 1062784273, 17607354955, 316012688213, 6108011298847, 126490611884013, 2794122884322635, 65578524701197341, 1629676370022564219, 42748628870263418761, 1180373377691425730235

Offset: 0

Author

Ilya Gutkovskiy, Aug 13 2020

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..426

Crossrefs

Cf. A000670, A032032, A124504, A232475, A337058.

Programs

Maple

S:= series(1/(2+x^3/6-exp(x)),x,31):
seq(coeff(S,x,i)*i!,i=0..30); # Robert Israel, Aug 28 2020

Mathematica

nmax = 20; CoefficientList[Series[1/(2 + x^3/6 - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = a[1] = 1; a[n_] := a[n] = n (a[n - 1] + (n - 1) a[n - 2]/2) + Sum[Binomial[n, k] a[n - k], {k, 4, n}]; Table[a[n], {n, 0, 20}]

Formula

a(0) = a(1) = 1; a(n) = n * (a(n-1) + (n-1) * a(n-2) / 2) + Sum_{k=4..n} binomial(n,k) * a(n-k).