A344493 a(n) = 1 + Sum_{k=0..n-6} binomial(n-5,k) * a(k).

1, 1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 64, 135, 308, 767, 2059, 5821, 16963, 50312, 151189, 460981, 1433634, 4578748, 15110212, 51704075, 183423444, 672385222, 2534056116, 9768179743, 38357842713, 153070136072, 620275332697, 2553688944713, 10696223834397, 45654239302087

Offset: 0

Author

Ilya Gutkovskiy, May 21 2021

Keywords

• nonn

Crossrefs

Cf. A000629, A210543, A344489, A344490, A344491, A344492.

Programs

Mathematica

a[n_] := a[n] = 1 + Sum[Binomial[n - 5, k] a[k] , {k, 0, n - 6}]; Table[a[n], {n, 0, 34}]
nmax = 34; A[] = 0; Do[A[x] = (1 + x^5 A[x/(1 - x)])/((1 - x) (1 + x^5)) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Formula

G.f. A(x) satisfies: A(x) = (1 + x^5 * A(x/(1 - x))) / ((1 - x) * (1 + x^5)).