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A307708 G.f. A(x) satisfies: A(x) = x*exp(Sum_{n>=1} Sum_{k>=1} n*a(n)*x^(n*k)/k). 2
0, 1, 1, 3, 12, 63, 396, 2917, 24425, 228827, 2367622, 26799874, 329366481, 4367857498, 62177776756, 945859958142, 15315466471574, 263041021397267, 4776856199304608, 91464926203961913, 1841802097153485730, 38912445829903177835, 860714999879617986231, 19892998348606063366793 (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 - x^n)^(n*a(n)).

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

EXAMPLE

G.f.: A(x) = x + x^2 + 3*x^3 + 12*x^4 + 63*x^5 + 396*x^6 + 2917*x^7 + 24425*x^8 + 228827*x^9 + 2367622*x^10 + ...

MATHEMATICA

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

CROSSREFS

Cf. A000081, A307709.

Sequence in context: A305536 A121123 A020123 * A308206 A264151 A186186

Adjacent sequences:  A307705 A307706 A307707 * A307709 A307710 A307711

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 23 2019

STATUS

approved

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Last modified August 18 20:02 EDT 2019. Contains 326109 sequences. (Running on oeis4.)