A196193 E.g.f.: 1 + Sum_{n>=1} x^n/n! * Product_{k=1..n} (exp(k*x)-1)/(exp(x)-1).

1, 1, 2, 9, 66, 680, 9255, 159446, 3369212, 85259280, 2535716685, 87301792270, 3436207077666, 153006997872664, 7639004900670507, 424334306389160090, 26050024400518079480, 1756998299539728910624, 129516073605566573413977

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..160

Example

E.g.f.: A(x) = 1 + x + 2*x^2/2! + 9*x^3/3! + 66*x^4/4! + 680*x^5/5! +...
where
A(x) = 1 + x*(exp(x)-1)/(exp(x)-1) + x^2/2!*(exp(x)-1)*(exp(2*x)-1)/(exp(x)-1)^2 + x^3/3!*(exp(x)-1)*(exp(2*x)-1)*(exp(3*x)-1)/(exp(x)-1)^3 +...
Equivalently,
A(x) = 1 + x + x^2/2!*(exp(x)+1) + x^3/3!*(exp(x)+1)*(exp(2*x)+exp(x)+1) + x^4/4!*(exp(x)+1)*(exp(2*x)+exp(x)+1)*(exp(3*x)+exp(2*x)+exp(x)+1) +...

Prog

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

Crossrefs

Cf. A196194.

Sequence in context: A259607 A214930 A089471 * A331817 A118804 A365995

Adjacent sequences: A196190 A196191 A196192 * A196194 A196195 A196196

Keyword

nonn

Author

Paul D. Hanna, Sep 28 2011

Status

approved