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!)
A193333 G.f.: 1 = Sum_{n>=0} a(n)*x^n / Product_{k=1..n+1} (1+k*x)^3. 3
1, 3, 21, 244, 4056, 88770, 2426553, 79893084, 3085719033, 137035475333, 6888543200172, 387050951446488, 24058512516152880, 1640162160152393778, 121746052707050425113, 9778208522585460239036, 845181303653928350311539, 78247854362736258482850285 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Compare to the g.f. for factorials: 1 = Sum_{n>=0} n!*x^n/Product_{k=1..n+1} (1+k*x).
LINKS
EXAMPLE
1 = 1/(1+x)^3 + 3*x/((1+x)^3*(1+2*x)^3) + 21*x^2/((1+x)^3*(1+2*x)^3*(1+3*x)^3) + 244*x^3/((1+x)^3*(1+2*x)^3*(1+3*x)^3*(1+4*x)^3) +...
PROG
(PARI) {a(n)=if(n==0, 1, polcoeff(1-sum(k=0, n-1, a(k)*x^k/prod(j=1, k+1, 1+j*x+x*O(x^n))^3), n))}
CROSSREFS
Sequence in context: A145083 A234303 A138213 * A290129 A365602 A371006
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 23 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 March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)