OFFSET
0,3
FORMULA
G.f.: A(x) = Sum_{n>=1} a(n)*x^n = x * Product_{n>=1} 1/(1 - x^n)^(a(n)+n).
Recurrence: a(n+1) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} d*(a(d) + d) ) * a(n-k+1).
EXAMPLE
G.f.: A(x) = x + 2*x^2 + 7*x^3 + 22*x^4 + 73*x^5 + 242*x^6 + 838*x^7 + 2951*x^8 + 10661*x^9 + 39169*x^10 + ...
MATHEMATICA
terms = 28; A[_] = 0; Do[A[x_] = x Exp[Sum[(A[x^k] + DivisorSigma[2, k] x^k)/k, {k, 1, terms}]] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x]
a[n_] := a[n] = SeriesCoefficient[x Product[1/(1 - x^k)^(a[k] + k), {k, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 0, 28}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 08 2019
STATUS
approved