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A196193 E.g.f.: 1 + Sum_{n>=1} x^n/n! * Product_{k=1..n} (exp(k*x)-1)/(exp(x)-1). 2
1, 1, 2, 9, 66, 680, 9255, 159446, 3369212, 85259280, 2535716685, 87301792270, 3436207077666, 153006997872664, 7639004900670507, 424334306389160090, 26050024400518079480, 1756998299539728910624, 129516073605566573413977 (list; graph; refs; listen; history; text; internal format)
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 A020555

Adjacent sequences:  A196190 A196191 A196192 * A196194 A196195 A196196

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 28 2011

STATUS

approved

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Last modified January 26 23:54 EST 2022. Contains 350601 sequences. (Running on oeis4.)