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A343523
a(0) = 1; a(n) = 2 * Sum_{k=1..n} binomial(n,k) * a(k-1).
7
1, 2, 8, 34, 164, 878, 5136, 32490, 220476, 1594470, 12223016, 98876322, 840804820, 7491247006, 69730182720, 676390547034, 6821988655468, 71398971351510, 774032400213336, 8677733804696594, 100459693769214980, 1199306075189097230, 14746332963835756400, 186534818943430728906
OFFSET
0,2
LINKS
FORMULA
G.f. A(x) satisfies: A(x) = 1 + 2 * x * A(x/(1 - x)) / (1 - x)^2.
MATHEMATICA
a[0] = 1; a[n_] := a[n] = 2 Sum[Binomial[n, k] a[k - 1], {k, 1, n}]; Table[a[n], {n, 0, 23}]
nmax = 23; A[_] = 0; Do[A[x_] = 1 + 2 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