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!)
A163826 G.f.: Sum_{n>=1} n * 2^(n^2) * x^n / (1 - 2^n*x)^(n+1). 1
2, 40, 1944, 314432, 189747360, 445551600000, 4129013201798016, 151656774720556632064, 22103008531040898656506368, 12788356812264101562500000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
More generally, we have the identity:
Sum_{n>=1} n*q^(n^2)*x^n/(1-q^n*xy)^(n+1) = Sum_{n>=1} n*q^n*(q^n+y)^(n-1)*x^n.
LINKS
FORMULA
a(n) = n * 2^n * (2^n + 1)^(n-1).
E.g.f.: Sum_{n>=1} n * 2^(n^2) * exp(2^n*x) * x^n/n!. - Paul D. Hanna, Jul 30 2014
EXAMPLE
G.f.: 2*x + 40*x^2 + 1944*x^3 + 314432*x^4 + 189747360*x^5 +...
MATHEMATICA
Table[n*2^n*(2^n + 1)^(n - 1), {n, 1, 25}] (* G. C. Greubel, Aug 05 2017 *)
PROG
(PARI) a(n)=n*2^n*(2^n+1)^(n-1)
for(n=0, 20, print1(a(n), ", "))
(PARI) {a(n)=polcoeff(sum(m=1, n, m*2^(m^2)*x^m/(1-2^m*x+x*O(x^(n-m)))^(m+1)), n)}
for(n=0, 20, print1(a(n), ", "))
(PARI) {a(n)=n!*polcoeff(sum(m=1, n, m*2^(m^2)*exp(2^m*x+x*O(x^(n-m)))*x^m/m!), n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
Sequence in context: A198248 A261732 A292418 * A000816 A000819 A060079
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 04 2009
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.)