A351283 - OEIS

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A351283

G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - x)) / (1 - x)^4.

1, 1, 1, 5, 16, 46, 142, 496, 1888, 7538, 31291, 135739, 617461, 2939215, 14575027, 75014471, 399901294, 2205630124, 12572140372, 73961880118, 448447331338, 2798640572516, 17956583819425, 118336081817953, 800278211629795, 5549154792085813, 39420390891260821

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..26.

FORMULA

a(0) = a(1) = 1; a(n) = Sum_{k=0..n-2} binomial(n+1,k+3) * a(k).

MATHEMATICA

nmax = 26; A[_] = 0; Do[A[x_] = 1 + x + x^2 A[x/(1 - x)]/(1 - x)^4 + 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 + 3] a[k], {k, 0, n - 2}]; Table[a[n], {n, 0, 26}]

CROSSREFS

Cf. A007476, A045499, A351437, A351438.