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A193478 G.f. A(x) satisfies: 1/(1-x) = Sum_{n>=0} A(x)^n/G(n), where A(x) = Sum_{n>=1} a(n)*x^n/G(n), and G(n) = Product_{k=0..n} k! is the Barnes G-function (A000178). 1
1, 1, 5, 95, 9959, 6270119, 28519938719, 1045680030158399, 349874346597600908159, 1178635679994967168072291199, 44013684086180240167822552866892799, 19826711369458419136710617483545735797772799, 116690731684609551482643899854886684445978037938815999 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..13.

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

EXAMPLE

A(x) = x + x^2/(1!*2!) + 5*x^3/(1!*2!*3!) + 95*x^4/(1!*2!*3!*4!) + 9959*x^5/(1!*2!*3!*4!*5!) + 6270119*x^6/(1!*2!*3!*4!*5!*6!) +...+ a(n)*x^n/G(n) +...

where

1/(1-x) = 1 + A(x) + A(x)^2/(1!*2!) + A(x)^3/(1!*2!*3!) + A(x)^4/(1!*2!*3!*4!) + A(x)^5/(1!*2!*3!*4!*5!) + A(x)^6/(1!*2!*3!*4!*5!*6!) +...+  A(x)^n/G(n) +...

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

PROG

(PARI) {a(n)=local(A=sum(m=1, n-1, a(m)*x^m/prod(k=0, m, k!))+O(x^(n+2)));

prod(k=0, n, k!)*polcoeff(1/(1-x)-sum(m=0, n, A^m/prod(k=0, m, k!)), n)}

CROSSREFS

Cf. A193479, A193440.

Sequence in context: A182960 A241998 A263394 * A218463 A192343 A152839

Adjacent sequences:  A193475 A193476 A193477 * A193479 A193480 A193481

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 27 2011

STATUS

approved

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Last modified February 24 22:57 EST 2020. Contains 332216 sequences. (Running on oeis4.)