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 A363467 G.f. A(x) satisfies: A(x) = x + x^2 * exp( Sum_{k>=1} (-1)^(k+1) * A(x^k)^3 / (k*x^(2*k)) ). 2
 1, 1, 1, 3, 9, 25, 88, 292, 1031, 3685, 13433, 49608, 185465, 699963, 2664650, 10217130, 39428179, 153009240, 596761737, 2337875430, 9195732624, 36301739221, 143780858517, 571191310205, 2275409450019, 9087376470138, 36377539265376, 145937953205705, 586645566919856 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Table of n, a(n) for n=1..29. MATHEMATICA nmax = 29; A[_] = 0; Do[A[x_] = x + x^2 Exp[Sum[(-1)^(k + 1) A[x^k]^3/(k x^(2 k)), {k, 1, nmax}]] + O[x]^(nmax + 1)//Normal, nmax + 1]; CoefficientList[A[x], x] // Rest a[1] = a[2] = 1; f[n_] := f[n] = Sum[a[k] a[n - k], {k, 1, n - 1}]; g[n_] := g[n] = Sum[a[k] f[n - k], {k, 1, n - 1}]; a[n_] := a[n] = (1/(n - 2)) Sum[Sum[(-1)^(k/d + 1) d g[d + 2], {d, Divisors[k]}] a[n - k], {k, 1, n - 2}]; Table[a[n], {n, 1, 29}] CROSSREFS Cf. A007560, A052755, A363388, A363465, A363468. Sequence in context: A217995 A246653 A192371 * A192465 A012771 A351891 Adjacent sequences: A363464 A363465 A363466 * A363468 A363469 A363470 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jun 03 2023 STATUS approved

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Last modified October 1 14:06 EDT 2023. Contains 365826 sequences. (Running on oeis4.)