A348701 a(n) = Sum_{x_1+x_2+x_3+x_4=n, 0 <= x_1 <=x_2 <= x_3 <= x_4 <= n} (3*n)!/((n-x_1)! * (n-x_2)! * (n-x_3)! * (n-x_4)!).

1, 6, 270, 14280, 1027950, 49945896, 3576428856, 206746398144, 14538815734014, 856120482145500, 57732481295380320, 3504640795033499160, 243836930413853027160, 14665028066155264295400, 977424087385506563672160, 61042393779786411602842080

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..535 (terms 0..200 from Seiichi Manyama)

Vaclav Kotesovec, Plot of a(n+1)/a(n) for n = 1..500

Mathematica

Table[Sum[If[a + b + c + d == n, (3 n)!/((n - a)!*(n - b)!*(n - c)!*(n - d)!), 0], {a, 0, n}, {b, 0, a}, {c, 0, b}, {d, 0, c}], {n, 0, 15}] (* Michael De Vlieger, Oct 30 2021 *)

Prog

(PARI) a(n) = sum(a=0, n, sum(b=a, n, sum(c=b, n, sum(d=c, n, if(a+b+c+d==n, (3*n)!/((n-a)!*(n-b)!*(n-c)!*(n-d)!), 0)))));

Crossrefs

Cf. A027306, A092473, A348704.

Cf. A348700.

Sequence in context: A221900 A229773 A193983 * A233234 A281694 A250390

Adjacent sequences: A348698 A348699 A348700 * A348702 A348703 A348704

Keyword

nonn

Author

Seiichi Manyama, Oct 30 2021

Status

approved