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
Keywords
Programs
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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]
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).