A336513 a(n) = Sum_{i=1..n} Product_{j=(i-1)*n+1..i*n} j.

1, 14, 630, 57264, 8626800, 1940869440, 609372212400, 254507088084480, 136432540607489280, 91303132805512992000, 74605774050426543724800, 73097485140038735163110400, 84588938888439008795675904000, 114144070365165930162064530739200, 177648727691418999798103189989120000

Offset: 1

Author

Seiichi Manyama, Jul 23 2020

Keywords

• nonn
• easy

Examples

			a(2) = 1*2 + 3*4 = 14.
a(3) = 1*2*3 + 4*5*6 + 7*8*9 = 630.
a(4) = 1*2*3*4 + 5*6*7*8 + 9*10*11*12 + 13*14*15*16 = 57264.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..214

Crossrefs

Main diagonal of A333446.

Cf. A096131, A336502.

Programs

Mathematica

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

PARI

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

Formula

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