A339027 - OEIS

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

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OFFSET

0,6

LINKS

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

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).

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}]

PROG