A092473
a(n) = Sum_{i+j+k=n, 0<=i<=j<=k<=n} (2n)!/((i+j)! * (j+k)! * (k+i)!).
Original entry on oeis.org
1, 2, 18, 170, 1330, 11382, 117810, 934362, 8611746, 82240730, 699393838, 6244164940, 59910383026, 507902083210, 4599466921410, 43063170064620, 372282144948450, 3338235118237410, 31231394376541650, 270058012725600000
Offset: 0
-
a(n)=sum(i=0,n,sum(j=0,i,sum(k=0,j,if(i+j+k-n,0,(2*n)!/(i+j)!/(j+k)!/(k+i)!))))
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)!).
Original entry on oeis.org
1, 24, 1440, 97440, 6745200, 467170704, 32179283136, 2201392866816, 149582010088368, 10100991172786800, 678330750569025840, 45330886561301259360, 3016323760677017743680, 199948320909528951802560, 13210188418741950461761920, 870202858863529042485373440
Offset: 0
-
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)))));
A348703
a(n) = Sum_{x_1+x_2+ ... +x_n=n, 0 <= x_1, x_2, ... , x_n <= n} ((n-1)*n)!/((n-x_1)! * (n-x_2)! * ... * (n-x_n)!).
Original entry on oeis.org
1, 1, 4, 510, 6745200, 19038823123320, 19549762329157865925120, 11131011767163918530071193512089600, 4977434038774545402380656971924547417738384800000
Offset: 0
-
def f(n)
return 1 if n < 2
(1..n).inject(:*)
end
def A(k, n)
sum = 0
m = f((k - 1) * n)
(0..n).to_a.repeated_permutation(k){|i|
if (0..k - 1).inject(0){|s, j| s + i[j]} == n
sum += m / (0..k - 1).inject(1){|s, j| s * f(n - i[j])}
end
}
sum
end
def A348703(n)
(0..n).map{|i| A(i, i)}
end
p A348703(7)
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