A307724 - OEIS

A307724

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

0, 1, 1, 3, 12, 64, 402, 2999, 25100, 236278, 2444779, 27725926, 340761474, 4522224643, 64378645709, 979609661544, 15862570817855, 272466359964053, 4948142926019039, 94748748685737418, 1907956061833749740, 40310880538563569017, 891655630401500129652, 20608302703021633063682

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Table of n, a(n) for n=0..23.

FORMULA

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

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

EXAMPLE

G.f.: A(x) = x + x^2 + 3*x^3 + 12*x^4 + 64*x^5 + 402*x^6 + 2999*x^7 + 25100*x^8 + 236278*x^9 + ...

MATHEMATICA

a[n_] := a[n] = SeriesCoefficient[x Exp[Sum[Sum[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}]

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

CROSSREFS

Cf. A093637, A307725.

Sequence in context: A326809 A326557 A308204 * A029851 A201720 A207557

Adjacent sequences: A307721 A307722 A307723 * A307725 A307726 A307727

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 24 2019

STATUS

approved