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!)
A361705 Constant term in the expansion of (1 + w^4 + x^4 + y^4 + z^4 + 1/(w*x*y*z))^n. 2
1, 1, 1, 1, 1, 1, 1, 1, 1681, 15121, 75601, 277201, 831601, 2162161, 5045041, 10810801, 54054001, 592191601, 5035670641, 31553973361, 157346607601, 660308770801, 2420415874801, 7951853614321, 24853781309281, 91246800876001, 497098157556001, 3346262924004001 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,9
LINKS
FORMULA
a(n) = Sum_{k=0..floor(n/8)} (4*k)!/k!^4 * binomial(8*k,4*k) * binomial(n,8*k).
a(n) ~ 5^(n+2) / (2^(5/2) * Pi^2 * n^2). - Vaclav Kotesovec, Mar 25 2023
MATHEMATICA
Table[Sum[(4*k)!/k!^4 * Binomial[8*k, 4*k] * Binomial[n, 8*k], {k, 0, n/8}], {n, 0, 30}] (* Vaclav Kotesovec, Mar 25 2023 *)
PROG
(PARI) a(n) = sum(k=0, n\8, (4*k)!/k!^4*binomial(8*k, 4*k)*binomial(n, 8*k));
CROSSREFS
Sequence in context: A228183 A175897 A370355 * A322745 A189654 A163009
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Mar 21 2023
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 February 26 06:43 EST 2024. Contains 370335 sequences. (Running on oeis4.)