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A363468 G.f. A(x) satisfies: A(x) = x + x^2 * exp( Sum_{k>=1} (-1)^(k+1) * A(x^k)^4 / (k*x^(3*k)) ). 2
1, 1, 1, 4, 14, 48, 201, 812, 3455, 14961, 65954, 294884, 1334526, 6098879, 28114885, 130561444, 610244889, 2868547475, 13552299256, 64316483918, 306473091394, 1465727378317, 7033293786125, 33851816310445, 163384902125185, 790589562321385, 3834540111072545, 18638976010097900 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
LINKS
MATHEMATICA
nmax = 28; A[_] = 0; Do[A[x_] = x + x^2 Exp[Sum[(-1)^(k + 1) A[x^k]^4/(k x^(3 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[f[k] f[n - k], {k, 1, n - 1}]; a[n_] := a[n] = (1/(n - 2)) Sum[Sum[(-1)^(k/d + 1)d g[d + 3], {d, Divisors[k]}] a[n - k], {k, 1, n - 2}]; Table[a[n], {n, 1, 28}]
CROSSREFS
Sequence in context: A047028 A220819 A047138 * A111299 A245824 A356121
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 03 2023
STATUS
approved

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Last modified April 16 12:05 EDT 2024. Contains 371711 sequences. (Running on oeis4.)