A352901 a(0) = 1; a(n) = Sum_{k=0..floor(n/3)} binomial(n+1,3*k+1) * a(k).
1, 2, 3, 6, 15, 36, 80, 172, 369, 796, 1727, 3774, 8322, 18528, 41643, 94460, 216121, 498186, 1155147, 2689626, 6278841, 14676900, 34316598, 80194032, 187195554, 436310190, 1015176726, 2357708258, 5465611759, 12647864454, 29219750157, 67403414568, 155276809533
Offset: 0
Keywords
Programs
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Mathematica
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n + 1, 3 k + 1] a[k], {k, 0, Floor[n/3]}]; Table[a[n], {n, 0, 32}] nmax = 32; A[] = 1; Do[A[x] = A[x^3/(1 - x)^3]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
Formula
G.f. A(x) satisfies: A(x) = A(x^3/(1 - x)^3) / (1 - x)^2.
E.g.f.: d/dx ( exp(x) * Sum_{n>=0} a(n) * x^(3*n+1) / (3*n+1)! ).
Comments