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A306729 a(n) = Product_{i=0..n, j=0..n} (i! + j!). 5
2, 16, 5184, 9559130112, 109045776752640000000000, 27488263744928988967331390258832998400000000000, 1147897050240877062218236820013018349788772091106840426434074807527014400000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..6.

FORMULA

a(n) ~ c * 2^(n^2/2 + 2*n) * Pi^(n^2/2 + n) * n^(2*n^3/3 + 2*n^2 + 11*n/6 + 5/2) / exp(8*n^3/9 + 2*n^2 + n), where c = A324569 = 62.14398692334529025548974541735...

a(n) = a(n-1) * A323717(n)^2 / (2*n!). - Vaclav Kotesovec, Mar 28 2019

MATHEMATICA

Table[Product[i! + j!, {i, 0, n}, {j, 0, n}], {n, 0, 7}]

Clear[a]; a[n_] := a[n] = If[n == 0, 2, a[n-1] * Product[k! + n!, {k, 0, n}]^2 / (2*n!)]; Table[a[n], {n, 0, 7}] (* Vaclav Kotesovec, Mar 27 2019 *)

Table[Product[Product[k! + j!, {k, 0, j}], {j, 1, n}]^2 / (2^(n-1) * BarnesG[n + 2]), {n, 0, 7}] (* Vaclav Kotesovec, Mar 27 2019 *)

PROG

(Python)

from math import prod, factorial as f

def a(n): return prod(f(i)+f(j) for i in range(n) for j in range(n))

print([a(n) for n in range(1, 8)]) # Michael S. Branicky, Feb 16 2021

CROSSREFS

Cf. A000178, A055462, A079478, A217757, A323717, A324403, A325052.

Sequence in context: A061301 A180962 A324565 * A325049 A334912 A092798

Adjacent sequences:  A306726 A306727 A306728 * A306730 A306731 A306732

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 06 2019

STATUS

approved

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Last modified August 1 06:45 EDT 2021. Contains 346384 sequences. (Running on oeis4.)