A267968 a(n) = Product_{k = 1..n} k^(k + 1).

1, 1, 8, 648, 663552, 10368000000, 2902376448000000, 16731622649806848000000, 2245680377810414777401344000000, 7830203310981140781182893575634944000000, 783020331098114078118289357563494400000000000000000, 2457453226667794121573260254679367673480373862400000000000000000

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..35

Formula

a(n) = n! * A002109(n). - Vaclav Kotesovec, Jan 26 2016

a(n) = (n!)^2 * abs(A203421(n)). - Michel Marcus, Feb 11 2016

Maple

a:= proc(n) a(n):= `if`(n=0, 1, a(n-1)*n^(n+1)) end:
seq(a(n), n=0..12);  # Alois P. Heinz, Feb 10 2016

Mathematica

a[n_]:= Product[k^(k+1), {k, n}]; Table[a[n], {n, 0, 20}]
Table[Hyperfactorial[n]*n!, {n, 0, 15}] (* Vaclav Kotesovec, Jan 26 2016 *)

Prog

(Magma) [&*[k^(k+1): k in [1..n]]: n in [1..11]]; // Vincenzo Librandi, Jan 23 2016
(PARI) a(n) = prod(k=1, n, k^(k+1)); \\ Michel Marcus, Jan 23 2016
(SageMath) [product(k^(k+1) for k in range(1, n+1)) for n in range(21)] # G. C. Greubel, Feb 18 2024

Crossrefs

Cf. A002109 (Product_{k = 1..n} k^k), A203421 (Product_{k = 1..n} k^(k-1), up to sign).

Sequence in context: A197045 A258385 A352593 * A253268 A235368 A247731

Adjacent sequences: A267965 A267966 A267967 * A267969 A267970 A267971

Keyword

nonn

Author

José María Grau Ribas, Jan 22 2016

Status

approved