OFFSET
0,2
FORMULA
G.f.: hypergeometric10F9([1/9, 1/6, 2/9, 1/3, 4/9, 5/9, 2/3, 7/9, 5/6, 8/9], [1/5, 1/5, 2/5, 2/5, 3/5, 3/5, 4/5, 4/5, 1], (167365651248*z)/9765625).
E.g.f.: hypergeometric10F10([1/9, 1/6, 2/9, 1/3, 4/9, 5/9, 2/3, 7/9, 5/6, 8/9], [1/5, 1/5, 2/5, 2/5, 3/5, 3/5, 4/5, 4/5, 1,1], (167365651248*z)/9765625).
a(n) = Integral_{x=0..167365651248/9765625} x^n*W(x) dx, n>=0, where W(x) = (1953125*MeijerG([[], [-4/5, -4/5, -3/5, -3/5, -2/5, -2/5, -1/5, -1/5, 0, 0]], [[-1/9, -1/6, -2/9, -1/3, -4/9, -5/9, -2/3, -7/9, -5/6, -8/9], []], (9765625*x)/167365651248))/(111577100832*Pi). MeijerG is the Meijer G - function. This integral representation as the n-th power moment of the W(x) function in the interval [0, 167365651248/9765625] is verified by direct integration. However, we are unable at present to determine the geometric shape of W(x).
MAPLE
seq((6*n)!*(9*n)!/((2*n)!*(3*n)!*((5*n)!)^2), n=0..12);
CROSSREFS
KEYWORD
nonn
AUTHOR
Karol A. Penson, Dec 29 2023
STATUS
approved