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A301831 G.f. A(x) satisfies: A(x) = Product_{k>=1} 1/(1 + x^k*A(x)^k)^k. 1
1, -1, 0, 0, 6, -16, 16, -34, 217, -681, 1343, -3466, 13370, -42380, 109477, -312448, 1040248, -3267138, 9447529, -28367596, 90504001, -283611105, 861087913, -2654231074, 8386506600, -26359974392, 81902319183, -256179313766, 809890745232, -2557697524240, 8046530976599 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..30.

FORMULA

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

a(n) = [x^n] (Sum_{k>=0} A255528(k)*x^k)^(n+1)/(n + 1).

EXAMPLE

G.f. A(x) = 1 - x + 6*x^4 - 16*x^5 + 16*x^6 - 34*x^7 + 217*x^8 - 681*x^9 + 1343*x^10 - 3466*x^11 + ...

log(A(x)) = -x - x^2/2 - x^3/3 + 23*x^4/4 - 51*x^5/5 + 35*x^6/6 - 197*x^7/7 + ... + A281266(n)*x^n/n + ...

CROSSREFS

Cf. A109085, A181315, A255528, A281266, A301455, A301456, A301624.

Sequence in context: A028286 A046629 A291795 * A183127 A222884 A230949

Adjacent sequences:  A301828 A301829 A301830 * A301832 A301833 A301834

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Mar 27 2018

STATUS

approved

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Last modified October 16 13:32 EDT 2019. Contains 328093 sequences. (Running on oeis4.)