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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 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.)