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A193440 exp( Sum_{n>=1} x^n/G(n) ) = Sum_{n>=0} a(n)/G(n), where G(n) = Product_{k=0..n} k! is the Barnes G-function of n (A000178). 2
1, 1, 2, 9, 145, 10489, 4182481, 10893144241, 213590500341121, 35762619247862532481, 57146369032805384396332801, 963199581177063129894232882156801, 187554502919537918586035198740350553881601, 458564976873147078680542618033293809080455988300801 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Sum_{n>=0} a(n)/G(n) = 4.88825080515459884947818345139584332...

LINKS

Table of n, a(n) for n=0..13.

Eric Weisstein's World of Mathematics, Barnes G-Function.

EXAMPLE

A(x) = 1 + x + 2*x^2/2 + 9*x^3/12 + 145*x^4/288 + 10489*x^5/34560 + 4182481*x^6/24883200 + 10893144241*x^7/125411328000 +...+ a(n)*x^n/G(n) +...

where

log(A(x)) = x + x^2/2 + x^3/12 + x^4/288 + x^5/34560 + x^6/24883200 + x^7/125411328000 +...+ x^n/G(n) +...

and G(n) = 0!*1!*2!*3!*...*(n-1)!*n!.

PROG

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

CROSSREFS

Cf. A000178.

Sequence in context: A110860 A050995 A174954 * A117116 A211935 A133468

Adjacent sequences:  A193437 A193438 A193439 * A193441 A193442 A193443

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 25 2011

STATUS

approved

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Last modified June 6 11:14 EDT 2020. Contains 334827 sequences. (Running on oeis4.)