login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A193479 G.f. A(x) satisfies: 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, -1, 5, -121, 16199, -13857481, 86631572159, -4470597876144961, 2126428452257713430399, -10305779379533133607589385601, 557802385738943120790269629003660799, -366846102335019802908345392106358106684889601, 3169417347948517943104654704100947667168800468999705599 (list; graph; refs; listen; history; text; internal format)
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!) - 121*x^4/(1!*2!*3!*4!) + 16199*x^5/(1!*2!*3!*4!*5!) - 13857481*x^6/(1!*2!*3!*4!*5!*6!) +...+ a(n)*x^n/sf(n) +...

where

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

CROSSREFS

Cf. A000178, A193478, A193440.

Sequence in context: A012151 A012156 A290167 * A324089 A071171 A113906

Adjacent sequences:  A193476 A193477 A193478 * A193480 A193481 A193482

KEYWORD

sign

AUTHOR

Paul D. Hanna, Jul 27 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 11 10:15 EDT 2022. Contains 356065 sequences. (Running on oeis4.)