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%I A307976 #6 May 08 2019 22:17:48
%S A307976 0,1,2,7,22,73,242,838,2951,10661,39169,146231,552791,2112791,8149184,
%T A307976 31683277,124030331,488484081,1934137711,7694617999,30742092365,
%U A307976 123294683460,496206766654,2003331980722,8111420525097,32929963668470,134012337268578,546609050991988,2234166616090803
%N A307976 G.f. A(x) satisfies: A(x) = x * exp(Sum_{k>=1} (A(x^k) + sigma_2(k)*x^k)/k).
%F A307976 G.f.: A(x) = Sum_{n>=1} a(n)*x^n = x * Product_{n>=1} 1/(1 - x^n)^(a(n)+n).
%F A307976 Recurrence: a(n+1) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} d*(a(d) + d) ) * a(n-k+1).
%e A307976 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 + ...
%t A307976 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]
%t A307976 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}]
%Y A307976 Cf. A000041, A000081, A000219, A001157, A307975.
%K A307976 nonn
%O A307976 0,3
%A A307976 _Ilya Gutkovskiy_, May 08 2019

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