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 A307725 G.f. A(x) satisfies: A(x) = x*exp(Sum_{n>=1} Sum_{k>=1} (-1)^(k+1)*n^k*a(n)^k*x^(n*k)/k). 1

%I

%S 0,1,1,2,8,38,234,1670,13730,126050,1286506,14374806,174922742,

%T 2299332974,32498831162,491302184254,7913576956058,135291701108082,

%U 2447171221364738,46693007367175606,937331324424610142,19748487304680389214,435735970210393888898,10048153760813576981702

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

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

%F Recurrence: a(n+1) = -(1/n) * Sum_{k=1..n} ( Sum_{d|k} d*(-d*a(d))^(k/d) ) * a(n-k+1).

%e G.f.: A(x) = x + x^2 + 2*x^3 + 8*x^4 + 38*x^5 + 234*x^6 + 1670*x^7 + 13730*x^8 + 126050*x^9 + ...

%t a[n_] := a[n] = SeriesCoefficient[x Exp[Sum[Sum[(-1)^(k + 1) j^k a[j]^k x^(j k)/k, {k, 1, n - 1}], {j, 1, n - 1}]], {x, 0, n}]; a[1] = 1; Table[a[n], {n, 0, 23}]

%t a[n_] := a[n] = SeriesCoefficient[x Product[(1 + k a[k] x^k), {k, 1, n - 1}], {x, 0, n}]; a[1] = 1; Table[a[n], {n, 0, 23}]

%Y Cf. A032305, A307724.

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Apr 24 2019

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Last modified October 20 20:13 EDT 2019. Contains 328272 sequences. (Running on oeis4.)