A348701 - OEIS

%I #28 Mar 27 2022 03:06:01

%S 1,6,270,14280,1027950,49945896,3576428856,206746398144,

%T 14538815734014,856120482145500,57732481295380320,3504640795033499160,

%U 243836930413853027160,14665028066155264295400,977424087385506563672160,61042393779786411602842080

%N 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)!).

%H Vaclav Kotesovec, <a href="/A348701/b348701.txt">Table of n, a(n) for n = 0..535</a> (terms 0..200 from Seiichi Manyama)

%H Vaclav Kotesovec, <a href="/A348701/a348701.jpg">Plot of a(n+1)/a(n) for n = 1..500</a>

%t 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 *)

%o (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)))));

%Y Cf. A027306, A092473, A348704.

%Y Cf. A348700.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 30 2021