A193440 exp( Sum_{n>=1} x^n/G(n) ) = Sum_{n>=0} a(n)*x^n/G(n), where G(n) = Product_{k=0..n} k! = BarnesG(n+2), (see A000178).

1, 1, 2, 9, 145, 10489, 4182481, 10893144241, 213590500341121, 35762619247862532481, 57146369032805384396332801, 963199581177063129894232882156801, 187554502919537918586035198740350553881601, 458564976873147078680542618033293809080455988300801

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!.

Mathematica

Table[BarnesG[n+2] * SeriesCoefficient[Exp[Sum[x^k/BarnesG[k+2], {k, 1, n}]], {x, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Apr 03 2021 *)

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: A370556 A050995 A174954 * A117116 A211935 A133468

Adjacent sequences: A193437 A193438 A193439 * A193441 A193442 A193443

Keyword

nonn

Author

Paul D. Hanna, Jul 25 2011

Extensions

Definition corrected by Vaclav Kotesovec, Apr 03 2021

Status

approved