A339027 E.g.f.: exp(2 * (exp(x) - 1 - x - x^2 / 2 - x^3 / 6 - x^4 / 24)).

1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 506, 1850, 5018, 12014, 26886, 1066782, 8193070, 42723722, 185108514, 719359762, 10426744914, 118490840686, 976376930502, 6583701431086, 38977418758494, 377188932759354, 4671829781287922, 51479602726372402, 483303800325691922

Offset: 0

Author

Ilya Gutkovskiy, Nov 20 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..576

Crossrefs

Cf. A001861, A057814, A194689, A339014, A339017.

Programs

Mathematica

nmax = 28; CoefficientList[Series[Exp[2 (Exp[x] - 1 - x - x^2/2 - x^3/6 - x^4/24)], {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, 5, n}]; Table[a[n], {n, 0, 28}]

PARI

my(x='x+O('x^30)); Vec(serlaplace(exp(2 * (exp(x) - 1 - x - x^2/2 - x^3/6 - x^4/24)))) \\ Michel Marcus, Nov 20 2020

Formula

a(0) = 1; a(n) = 2 * Sum_{k=5..n} binomial(n-1,k-1) * a(n-k).

a(n) = Sum_{k=0..n} binomial(n,k) * A057814(k) * A057814(n-k).