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A339017
E.g.f.: exp(2 * (exp(x) - 1 - x - x^2 / 2 - x^3 / 6)).
4
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
0,5
LINKS
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).
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}]
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 19 2020
STATUS
approved