OFFSET
0,2
COMMENTS
Partial sums of A008977.
In general, for m > 1, Sum_{k=0..n} (m*k)!/k!^m ~ m^(m*n + m + 1/2) / ((m^m - 1) * (2*Pi*n)^((m-1)/2)). - Vaclav Kotesovec, Feb 28 2021
FORMULA
a(n) ~ 2^(8*n + 15/2) / (255 * Pi^(3/2) * n^(3/2)). - Vaclav Kotesovec, Feb 28 2021
D-finite with recurrence (n^3*a(n) +(-257*n^3+384*n^2-176*n+24)*a(n-1) +8*(4*n-3)*(2*n-1)*(4*n-1)*a(n-2)=0. - R. J. Mathar, Dec 04 2023
MAPLE
A342107 := proc(n)
add((4*k)!/k!^4, k=0..n) ;
end proc:
seq(A342107(n), n=0..70) ; # R. J. Mathar, Dec 04 2023
MATHEMATICA
Table[Sum[(4*k)!/k!^4, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Feb 28 2021 *)
PROG
(PARI) a(n) = sum(k=0, n, (4*k)!/k!^4);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Feb 28 2021
STATUS
approved