A203039 a(n) = [x^n/n!] 1 - (1-x)^(1/(1 + n*log(1-x))).

1, 4, 54, 1528, 74200, 5513088, 581644210, 82684556736, 15235237204524, 3531551323602720, 1005740523344585424, 345183221074356437760, 140516542507328903804616, 66939548487495601942276224, 36891997133237736166187224200

Offset

1,2

Links

Table of n, a(n) for n=1..15.

Formula

a(n) equals the coefficient of x^n/n! in the n-th iteration of 1 - (1-x)^(1/(1 + log(1-x))).

Example

 Let G(x) = 1 - (1-x)^(1/(1 + log(1-x))); the iterations of G(x) begin:
G(x) = x + 2*x^2/2! + 6*x^3/3! + 22*x^4/4! + 80*x^5/5! + 98*x^6/6! +...
G(G(x)) = x + 4*x^2/2! + 24*x^3/3! + 188*x^4/4! + 1780*x^5/5! +...
G(G(G(x))) = x + 6*x^2/2! + 54*x^3/3! + 642*x^4/4! + 9420*x^5/5! +...
G(G(G(G(x)))) = x + 8*x^2/2! + 96*x^3/3! + 1528*x^4/4! + 30200*x^5/5! +...
G(G(G(G(G(x))))) = x + 10*x^2/2! + 150*x^3/3! + 2990*x^4/4! + 74200*x^5/5! +...

Prog

 (PARI) {a(n)=n!*polcoeff(1-(1-x+x*O(x^n))^(1/(1+n*log(1-x+x*O(x^n)))), n)}

Crossrefs

Cf. A203038.

Sequence in context: A138459 A111161 A216733 * A369569 A201731 A225823

Adjacent sequences: A203036 A203037 A203038 * A203040 A203041 A203042

Keyword

nonn

Author

Paul D. Hanna, Dec 27 2011

Status

approved