The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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!)
A210438 G.f.: Sum_{n>=0} x^n * Product_{k=1..n} (k^2 + x) / (1 + k^2*x + x^2). 2
1, 1, 4, 20, 174, 2262, 40894, 980590, 30095022, 1149982990, 53521460958, 2980006437662, 195562339712590, 14936971352026094, 1313606920832545022, 131776096083434471678, 14956389843996883667182, 1906794751364126563388238, 271321222225812454677233694 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Compare to the identity:
Sum_{n>=0} x^n * Product_{k=1..n} (k + x) / (1 + k*x + x^2) = (1+x^2)/(1-x).
LINKS
FORMULA
a(n) ~ 2^(2*n+5) * n^(2*n+5/2) / (exp(2*n) * Pi^(2*n+3/2)). - Vaclav Kotesovec, Nov 02 2014
EXAMPLE
G.f.: A(x) = 1 + x + 4*x^2 + 20*x^3 + 174*x^4 + 2262*x^5 + 40894*x^6 +...
where
A(x) = 1 + x*(1+x)/(1+x+x^2) + x^2*(1+x)*(4+x)/((1+x+x^2)*(1+4*x+x^2)) + x^3*(1+x)*(4+x)*(9+x)/((1+x+x^2)*(1+4*x+x^2)*(1+9*x+x^2)) + x^4*(1+x)*(4+x)*(9+x)*(16+x)/((1+x+x^2)*(1+4*x+x^2)*(1+9*x+x^2)*(1+16*x+x^2)) +...
PROG
(PARI) {a(n)=polcoeff( sum(m=0, n, x^m*prod(k=1, m, (k^2+x)/(1+k^2*x+x^2 +x*O(x^n))) ), n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
Sequence in context: A366639 A068965 A185672 * A054474 A364344 A368455
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 19 2013
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 June 12 14:48 EDT 2024. Contains 373331 sequences. (Running on oeis4.)