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A345081
a(0) = 1; a(n) = 8 * Sum_{k=1..n} binomial(n,k) * a(k-1).
6
1, 8, 80, 856, 9824, 119912, 1547376, 21007992, 298874496, 4440618120, 68706037904, 1104224971416, 18394192882336, 316974497161384, 5640790811468976, 103503851543959224, 1955546066369814208, 37994858794236710088, 758272809049577019600, 15527828509092566876888
OFFSET
0,2
FORMULA
G.f. A(x) satisfies: A(x) = 1 + 8 * x * A(x/(1 - x)) / (1 - x)^2.
MATHEMATICA
a[0] = 1; a[n_] := a[n] = 8 Sum[Binomial[n, k] a[k - 1], {k, 1, n}]; Table[a[n], {n, 0, 19}]
nmax = 19; A[_] = 0; Do[A[x_] = 1 + 8 x A[x/(1 - x)]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 07 2021
STATUS
approved