A348700 - OEIS

A348700

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, 24, 1440, 97440, 6745200, 467170704, 32179283136, 2201392866816, 149582010088368, 10100991172786800, 678330750569025840, 45330886561301259360, 3016323760677017743680, 199948320909528951802560, 13210188418741950461761920, 870202858863529042485373440

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..250

FORMULA

From Vaclav Kotesovec, Oct 30 2021: (Start)

Recurrence: 2*(n-1)*n^2*(2*n - 1)*(65*n^5 - 1089*n^4 + 6575*n^3 - 18383*n^2 + 23840*n - 11584)*a(n) = (n-1)*(46475*n^8 - 823810*n^7 + 5577254*n^6 - 19173000*n^5 + 36602535*n^4 - 39648950*n^3 + 23762600*n^2 - 7257792*n + 875520)*a(n-1) - 6*(3*n - 5)*(3*n - 4)*(51155*n^7 - 830003*n^6 + 5035067*n^5 - 15152773*n^4 + 24453658*n^3 - 20908896*n^2 + 8592448*n - 1337856)*a(n-2) + 10368*(3*n - 8)*(3*n - 7)*(3*n - 5)*(3*n - 4)*(65*n^5 - 764*n^4 + 2869*n^3 - 4542*n^2 + 2768*n - 576)*a(n-3).

a(n) ~ 64^n. (End)

PROG

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

CROSSREFS

Cf. A000079, A092472, A348703.

Cf. A348701.

Sequence in context: A347857 A187852 A276595 * A010797 A260784 A099060

Adjacent sequences: A348697 A348698 A348699 * A348701 A348702 A348703

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Oct 30 2021

STATUS

approved