A295469 a(n) = (20*n)!*(3*n)!/((12*n)!*(10*n)!*n!).

1, 8398, 194588550, 5100249334348, 141026130105441350, 4018577033905015730148, 116743212747975158088926364, 3437433902477818949422435085400, 102221680117258170626629637553328710, 3063070065565412402561157982751304224500, 92339640658637142866394391974518333925957300

Offset: 0

Author

Gheorghe Coserea, Nov 28 2017

Keywords

• nonn

Crossrefs

Cf. A295431.

Programs

Maple

A295469 := proc(n)
    (20*n)!*(3*n)!/((12*n)!*(10*n)!*n!) ;
end proc:
seq(A295469(n),n=0..43) ; # R. J. Mathar, Jul 27 2022

Formula

G.f.: hypergeom([1/20, 3/20, 7/20, 9/20, 11/20, 13/20, 17/20, 19/20], [1/12, 1/6, 5/12, 1/2, 7/12, 5/6, 11/12], 625000000/19683*x).

D-finite with recurrence +27*n*(12*n-11)*(12*n-1)*(6*n-1)*(12*n-5)*(2*n-1)*(12*n-7)*(6*n-5)*a(n) -50*(20*n-11)*(20*n-9)*(20*n-7)*(20*n-3)*(20*n-1)*(20*n-19)*(20*n-17)*(20*n-13)*a(n-1)=0. - R. J. Mathar, Jul 27 2022