A349480 a(n) = Sum_{j=0..n} (-1)^(n-j) * Product_{k=(j-1)*n+1..j*n} k.

1, 1, 10, 390, 33456, 4845360, 1059099840, 325460948400, 133697543616000, 70733019878196480, 46831083260349024000, 37927830201482962540800, 36883442511877368877747200, 42409212946187708288828160000

Offset: 0

Author

Seiichi Manyama, Nov 19 2021

Keywords

• nonn

Examples

			a(2) = -1*2 + 3*4 = 10.
a(3) = 1*2*3 - 4*5*6 + 7*8*9 = 390.
a(4) = -1*2*3*4 + 5*6*7*8 - 9*10*11*12 + 13*14*15*16 = 33456.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..214

Crossrefs

Cf. A336513, A349470.

Programs

Mathematica

a[n_] := n! * Sum[(-1)^(n - k) * Binomial[k*n, n], {k, 0, n}]; Array[a, 14, 0] (* Amiram Eldar, Nov 19 2021 *)

PARI

a(n) = sum(j=0, n, (-1)^(n-j)*prod(k=(j-1)*n+1, j*n, k));

Formula

a(n) = n! * A349470(n) = n! * Sum_{k=0..n} (-1)^(n-k) * binomial(k*n,n).