A301578 - OEIS

A301578

G.f. A(x) satisfies: A(x) = Product_{k>=1} (1 + k*x^k*A(x)^k).

1, 1, 3, 12, 48, 211, 970, 4594, 22311, 110473, 555561, 2829918, 14570666, 75708835, 396481070, 2090558864, 11089276706, 59135014252, 316836936662, 1704764660218, 9207671377450, 49904141524184, 271325301723223, 1479427708380368, 8088057338101442, 44325245804200151

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..25.

EXAMPLE

G.f. A(x) = 1 + x + 3*x^2 + 12*x^3 + 48*x^4 + 211*x^5 + 970*x^6 + 4594*x^7 + 22311*x^8 + 110473*x^9 + ...

G.f. A(x) satisfies: A(x) = (1 + x*A(x)) * (1 + 2*x^2*A(x)^2) * (1 + 3*x^3*A(x)^3) * (1 + 4*x^4*A(x)^4) * ...

log(A(x)) = x + 5*x^2/2 + 28*x^3/3 + 137*x^4/4 + 726*x^5/5 + 3896*x^6/6 + 21071*x^7/7 + 115089*x^8/8 + ... + A297322(n)*x^n/n + ...

CROSSREFS

Cf. A022629, A181315, A297322, A301456, A301577.

Sequence in context: A165328 A351282 A142873 * A151168 A151169 A058371

Adjacent sequences: A301575 A301576 A301577 * A301579 A301580 A301581

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 23 2018

STATUS

approved