A352862 a(n) = 1 + Sum_{k=0..n-1} binomial(n+3,k+4) * a(k).

1, 2, 8, 36, 170, 865, 4742, 27757, 172375, 1130865, 7809057, 56572404, 428710587, 3389749264, 27901667938, 238599540142, 2115876327408, 19425465343555, 184355895494512, 1806122902809371, 18242807108024625, 189750478368293523, 2030261803964224359, 22323607721661782198

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Formula

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

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

Mathematica

a[n_] := a[n] = 1 + Sum[Binomial[n + 3, k + 4] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 23}]
nmax = 23; A[_] = 0; Do[A[x_] = 1/(1 - x) + x A[x/(1 - x)]/(1 - x)^5 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A000110, A032346, A032347, A045499, A045500, A186021, A352861.

Sequence in context: A084868 A350645 A330793 * A109980 A186338 A190862

Adjacent sequences: A352859 A352860 A352861 * A352863 A352864 A352865

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 06 2022

Status

approved