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 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)!). 3
 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

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Last modified May 20 23:05 EDT 2022. Contains 353886 sequences. (Running on oeis4.)