A073478 Expansion of (1+x)^(1/(1-x)).

1, 1, 2, 9, 44, 290, 2154, 19026, 186752, 2070792, 25119720, 334960560, 4824346152, 75100568088, 1250180063664, 22235660291880, 419595248663040, 8388866239417920, 176823515257447104, 3923498370610292544

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

E.g.f.: exp( Sum_{n>=1} x^n * Sum_{k=1..n} -(-1)^k/k ). - Paul D. Hanna, Jan 08 2014

a(n) ~ (log(2))^(1/4) * exp(2*sqrt(n*log(2)) - n - 1/2) * n^(n-1/4). - Vaclav Kotesovec, Apr 21 2014

Mathematica

CoefficientList[Series[(1+x)^(1/(1-x)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Apr 21 2014 *)

Prog

(PARI) {a(n)=n!*polcoeff((1+x +x*O(x^n))^(1/(1-x)), n)} \\ Paul D. Hanna, Jan 08 2014
(PARI) {a(n)=local(A); A=exp(sum(m=1, n, sum(k=1, m, -(-1)^k/k)*x^m)+x*O(x^n)); n!*polcoeff(A, n)} \\ Paul D. Hanna, Jan 08 2014

Crossrefs

Cf. A007113, A007120, A087761.

Sequence in context: A347571 A331559 A184932 * A336400 A360684 A357682

Adjacent sequences: A073475 A073476 A073477 * A073479 A073480 A073481

Keyword

nonn

Author

Vladeta Jovovic, Aug 26 2002

Extensions

More terms from Robert G. Wilson v, Aug 28 2002

Status

approved