A308227 G.f.: (x/(1 - x)) * Product_{k>=1} ((1 + x^k)/(1 - x^k))^a(k).

1, 3, 11, 47, 217, 1065, 5453, 28789, 155633, 857207, 4793103, 27136555, 155249971, 896133487, 5212477023, 30522169103, 179777122393, 1064411910393, 6331361864657, 37817265028841, 226731778956181, 1363993567341257, 8231111557650837, 49812263080757845

Offset: 1

Author

Ilya Gutkovskiy, May 16 2019

Keywords

• nonn

Crossrefs

Cf. A029856, A036249, A052829, A073075.

Programs

Mathematica

a[n_] := a[n] = SeriesCoefficient[x/(1 - x) Product[((1 + x^k)/(1 - x^k))^a[k], {k, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 24}]
terms = 24; A[] = 0; Do[A[x] = x Exp[Sum[2 A[x^(2 k - 1)]/(2 k - 1) + x^k/k, {k, 1, terms}]] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x] // Rest

Formula

G.f. A(x) satisfies: A(x) = x * exp(Sum_{k>=1} 2*A(x^(2*k-1))/(2*k - 1) + x^k/k).