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A351437
G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - x)) / (1 - x)^2.
7
1, 1, 1, 3, 7, 17, 47, 145, 481, 1691, 6295, 24805, 103095, 449805, 2052081, 9762699, 48334855, 248568321, 1325297879, 7312927481, 41694974649, 245288605059, 1487041552343, 9279329735685, 59537092965663, 392371097100373, 2653606218921673, 18400405626141667, 130712743774279015
OFFSET
0,4
FORMULA
a(0) = a(1) = 1; a(n) = Sum_{k=0..n-2} binomial(n-1,k+1) * a(k).
MATHEMATICA
nmax = 28; A[_] = 0; Do[A[x_] = 1 + x + x^2 A[x/(1 - x)]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = a[1] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k + 1] a[k], {k, 0, n - 2}]; Table[a[n], {n, 0, 28}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 11 2022
STATUS
approved