The On-Line Encyclopedia of Integer Sequences (OEIS)

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A345241

G.f. A(x) satisfies: A(x) = x + x^2 * exp(3 * Sum_{k>=1} A(x^k) / k).
(history; published version)

#6 by Alois P. Heinz at Fri Jun 11 21:15:57 EDT 2021

STATUS

proposed

approved

#5 by Ilya Gutkovskiy at Fri Jun 11 19:52:53 EDT 2021

STATUS

editing

proposed

#4 by Ilya Gutkovskiy at Fri Jun 11 19:23:20 EDT 2021

NAME

G.f. A(x) satisfies: A(x) = x + x^2 * exp(3 * Sum_{k>=1} A(x^k) / k).

#3 by Ilya Gutkovskiy at Fri Jun 11 19:05:28 EDT 2021

CROSSREFS

Cf. A006964, A007562, A345200, A345242.

#2 by Ilya Gutkovskiy at Fri Jun 11 19:00:37 EDT 2021

NAME

allocated for Ilya Gutkovskiy

G.f. A(x) satisfies: A(x) = x + x^2 * exp(3 * Sum{k>=1} A(x^k) / k).

DATA

1, 1, 3, 9, 28, 93, 315, 1109, 3969, 14505, 53726, 201588, 764001, 2921730, 11257881, 43669590, 170383933, 668236581, 2632898016, 10416893159, 41368099791, 164841324837, 658883345595, 2641064296638, 10613953319448, 42757746556377, 172628891937513, 698398635475974

OFFSET

1,3

FORMULA

G.f.: x + x^2 / Product_{n>=1} (1 - x^n)^(3*a(n)).

a(n+2) = (3/n) * Sum_{k=1..n} ( Sum_{d|k} d * a(d) ) * a(n-k+2).

MATHEMATICA

nmax = 28; A[_] = 0; Do[A[x_] = x + x^2 Exp[3 Sum[A[x^k]/k, {k, 1, nmax}]] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest

a[1] = a[2] = 1; a[n_] := a[n] = (3/(n - 2)) Sum[Sum[d a[d], {d, Divisors[k]}] a[n - k], {k, 1, n - 2}]; Table[a[n], {n, 1, 28}]

CROSSREFS

Cf. A006964, A007562.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Jun 11 2021

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Fri Jun 11 19:00:37 EDT 2021

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved