A307722 G.f. A(x) satisfies: A(x) = x*exp(2*Sum_{n>=1} Sum_{k>=1} n*a(n)*x^(n*(2*k-1))/(2*k - 1)).

0, 1, 2, 10, 78, 794, 9870, 143610, 2382350, 44266538, 909575170, 20468012850, 500542618118, 13218631046786, 374965272837542, 11372416113131346, 367296622702990270, 12587154399475110546, 456238999451039779510, 17440439387336903608866, 701272672299320517560470

Offset: 0

Author

Ilya Gutkovskiy, Apr 24 2019

Keywords

• nonn

Examples

			G.f.: A(x) = x + 2*x^2 + 10*x^3 + 78*x^4 + 794*x^5 + 9870*x^6 + 143610*x^7 + 2382350*x^8 + 44266538*x^9 + ...
		

Crossrefs

Cf. A073075, A307708, A307709.

Programs

Mathematica

a[n_] := a[n] = SeriesCoefficient[x Exp[2 Sum[Sum[j a[j] x^(j (2 k - 1))/(2 k - 1), {k, 1, n - 1}], {j, 1, n - 1}]], {x, 0, n}]; a[1] = 1; Table[a[n], {n, 0, 20}]
a[n_] := a[n] = SeriesCoefficient[x Product[((1 + x^k)/(1 - x^k))^(k a[k]), {k, 1, n - 1}], {x, 0, n}]; a[1] = 1; Table[a[n], {n, 0, 20}]

Formula

G.f.: A(x) = Sum_{n>=1} a(n)*x^n = x * Product_{n>=1} ((1 + x^n)/(1 - x^n))^(n*a(n)).