A202203 E.g.f.: Sum_{n>=0} 1/n! * Product_{k=1..n} -log(1-x^k).

1, 1, 1, 5, 12, 74, 420, 2904, 19880, 210384, 1844640, 20910240, 242478720, 3193551360, 41853651840, 682405788960, 9824634892800, 173309920358400, 3095955573419520, 58684751375685120, 1111152812649062400, 24883693662159360000, 514031737571893094400

Offset

0,4

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..390

Example

E.g.f.: A(x) = 1 + x + x^2/2! + 5*x^3/3! + 12*x^4/4! + 74*x^5/5! +...
A(x) = 1 - log(1-x) + log(1-x)*log(1-x^2)/2! - log(1-x)*log(1-x^2)*log(1-x^3)/3! + log(1-x)*log(1-x^2)*log(1-x^3)*log(1-x^4)/4! +...

Prog

(PARI) {a(n)=n!*polcoeff(1+sum(m=1, sqrt(2*n+1), (1/m!)*prod(k=1, m, -log(1-x^k +x*O(x^n)))), n)}

Crossrefs

Cf. A191461.

Sequence in context: A209481 A209340 A128323 * A074245 A235939 A215866

Adjacent sequences: A202200 A202201 A202202 * A202204 A202205 A202206

Keyword

nonn

Author

Paul D. Hanna, Dec 14 2011

Status

approved