A308946 Expansion of e.g.f. 1/(1 - x*(1 + x/2)*exp(x)).

1, 1, 5, 30, 244, 2485, 30351, 432502, 7043660, 129050649, 2627117875, 58829021416, 1437117395946, 38032508860177, 1083932872119839, 33098858988564090, 1078083456543449416, 37309607437056658129, 1367138649165397662627, 52879280631976735387588

Offset

0,3

Links

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

Formula

E.g.f.: 1 / (1 - Sum_{k>=1} (k*(k + 1)/2)*x^k/k!).

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * A000217(k) * a(n-k).

a(n) ~ n! * (2 + r) / ((2 + 4*r + r^2) * r^n), where r = 0.49122518354447387971550543450091640839121607... is the root of the equation exp(r)*r*(2 + r) = 2. - Vaclav Kotesovec, Aug 09 2021

Mathematica

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

Crossrefs

Cf. A000217, A001793, A006153, A052529, A279361, A308861.

Sequence in context: A201368 A072213 A257741 * A346681 A279155 A245247

Adjacent sequences: A308943 A308944 A308945 * A308947 A308948 A308949

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 02 2019

Status

approved