login
A336513
a(n) = Sum_{i=1..n} Product_{j=(i-1)*n+1..i*n} j.
4
1, 14, 630, 57264, 8626800, 1940869440, 609372212400, 254507088084480, 136432540607489280, 91303132805512992000, 74605774050426543724800, 73097485140038735163110400, 84588938888439008795675904000, 114144070365165930162064530739200, 177648727691418999798103189989120000
OFFSET
1,2
LINKS
FORMULA
a(n) = n! * A096131(n) = n! * Sum_{k=1..n} binomial(k*n, n).
EXAMPLE
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.
MATHEMATICA
a[n_] := n! * Sum[Binomial[k*n, n], {k, 1, n}]; Array[a, 15] (* Amiram Eldar, May 01 2021 *)
PROG
(PARI) {a(n) = sum(i=1, n, prod(j=(i-1)*n+1, i*n, j))}
CROSSREFS
Main diagonal of A333446.
Sequence in context: A283780 A210808 A139196 * A233078 A223129 A303288
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jul 23 2020
STATUS
approved