A339017 E.g.f.: exp(2 * (exp(x) - 1 - x - x^2 / 2 - x^3 / 6)).

1, 0, 0, 0, 2, 2, 2, 2, 142, 506, 1346, 3170, 53198, 375234, 1880738, 7919082, 72104190, 678488362, 5164781154, 33220643026, 271431061614, 2710340281426, 26278673924322, 228727591600826, 2081516848032222, 21560234032116154, 236863265302626722, 2521687569105476002

Offset: 0

Author

Ilya Gutkovskiy, Nov 19 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..569

Crossrefs

Cf. A001861, A057837, A194689, A339014, A339027.

Programs

Mathematica

nmax = 27; CoefficientList[Series[Exp[2 (Exp[x] - 1 - x - x^2/2 - x^3/6)], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = 2 Sum[Binomial[n - 1, k - 1] a[n - k], {k, 4, n}]; Table[a[n], {n, 0, 27}]

PARI

my(x='x+O('x^30)); Vec(serlaplace(exp(2*(exp(x) - 1 - x - x^2/2 - x^3/6)))) \\ Michel Marcus, Nov 19 2020

Formula

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

a(n) = Sum_{k=0..n} binomial(n,k) * A057837(k) * A057837(n-k).