A336513 - OEIS

%I #19 May 01 2021 17:41:14

%S 1,14,630,57264,8626800,1940869440,609372212400,254507088084480,

%T 136432540607489280,91303132805512992000,74605774050426543724800,

%U 73097485140038735163110400,84588938888439008795675904000,114144070365165930162064530739200,177648727691418999798103189989120000

%N a(n) = Sum_{i=1..n} Product_{j=(i-1)*n+1..i*n} j.

%H Seiichi Manyama, <a href="/A336513/b336513.txt">Table of n, a(n) for n = 1..214</a>

%F a(n) = n! * A096131(n) = n! * Sum_{k=1..n} binomial(k*n, n).

%e a(2) = 1*2 + 3*4 = 14.

%e a(3) = 1*2*3 + 4*5*6 + 7*8*9 = 630.

%e a(4) = 1*2*3*4 + 5*6*7*8 + 9*10*11*12 + 13*14*15*16 = 57264.

%t a[n_] := n! * Sum[Binomial[k*n, n], {k, 1, n}]; Array[a, 15] (* _Amiram Eldar_, May 01 2021 *)

%o (PARI) {a(n) = sum(i=1, n, prod(j=(i-1)*n+1,i*n, j))}

%Y Main diagonal of A333446.

%Y Cf. A096131, A336502.

%K nonn,easy

%O 1,2

%A _Seiichi Manyama_, Jul 23 2020