A193478 G.f. A(x) satisfies: 1/(1-x) = Sum_{n>=0} A(x)^n/sf(n), where A(x) = Sum_{n>=1} a(n)*x^n/sf(n), and sf(n) = Product_{k=0..n} k! is the superfactorial of n (A000178).

1, 1, 5, 95, 9959, 6270119, 28519938719, 1045680030158399, 349874346597600908159, 1178635679994967168072291199, 44013684086180240167822552866892799, 19826711369458419136710617483545735797772799, 116690731684609551482643899854886684445978037938815999

Offset

1,3

Links

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

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/sf(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/sf(n) +...
and sf(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. A000178, A193479, A193440.

Sequence in context: A241998 A263394 A336942 * A218463 A192343 A152839

Adjacent sequences: A193475 A193476 A193477 * A193479 A193480 A193481

Keyword

nonn

Author

Paul D. Hanna, Jul 27 2011

Status

approved