A336960 E.g.f.: 1 / (1 - x * (2 + x) * exp(x)).

1, 2, 14, 132, 1676, 26590, 506202, 11242952, 285383240, 8149464954, 258575410190, 9024809281972, 343619185754748, 14173557899208422, 629600469603730562, 29965010056866657600, 1521221783964264806672, 82053967063309770102130, 4686301361507067542636694

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

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

a(n) ~ n! * (2 + r) / ((2 + 4*r + r^2) * r^n), where r = 0.31516782494427474715049117135360576083681438371... is the root of the equation exp(r) * r * (2 + r) = 1. - Vaclav Kotesovec, Aug 09 2021

Mathematica

nmax = 18; CoefficientList[Series[1/(1 - x (2 + x) Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] k (k + 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]

Crossrefs

Cf. A002378, A006153, A308861, A308946, A336961.

Sequence in context: A246481 A048990 A089602 * A052641 A157085 A073553

Adjacent sequences: A336957 A336958 A336959 * A336961 A336962 A336963

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 09 2020

Status

approved