A306729
a(n) = Product_{i=0..n, j=0..n} (i! + j!).
Original entry on oeis.org
2, 16, 5184, 9559130112, 109045776752640000000000, 27488263744928988967331390258832998400000000000, 1147897050240877062218236820013018349788772091106840426434074807527014400000000000000
Offset: 0
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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 *)
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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
A203483
a(n) = v(n+1)/v(n), where v = A203482.
Original entry on oeis.org
3, 56, 19500, 267841728, 236189890379520, 19303349192505048268800, 199126474924007956512865886208000, 339543987407937097660189431863908761600000000, 121553118121801544803671246298148699436481551316864204800000
Offset: 1
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[(&*[Factorial(k) + Factorial(n+1): k in [1..n]]): n in [1..16]]; // G. C. Greubel, Aug 29 2023
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(* First program *)
f[j_]:= j!; z = 10;
v[n_]:= Product[Product[f[k] + f[j], {j,k-1}], {k,2,n}]
d[n_]:= Product[(i-1)!, {i, n}] (* A000178 *)
Table[v[n], {n,z}] (* A203482 *)
Table[v[n+1]/v[n], {n,z-1}] (* this sequence *)
Table[v[n]/d[n], {n,10}] (* A203510 *)
(* Second program *)
Table[Product[k!+(n+1)!, {k,n}], {n,15}] (* G. C. Greubel, Aug 29 2023 *)
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[product(factorial(k) + factorial(n+1) for k in range(1,n+1)) for n in range(1,16)] # G. C. Greubel, Aug 29 2023
Original entry on oeis.org
1, 1, 20, 9108, 153675648, 153926018668800, 13624548214772203315200, 148312029363286484759480524800000, 262925014428462931164318003384701335633920000, 96950311125839455466119755365478799838570665250861875200000
Offset: 0
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F:= Factorial; [1] cat [(&*[F(n+1) - F(j): j in [1..n]]): n in [1..20]]; // G. C. Greubel, Aug 30 2023
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(* First program *)
f[j_]:= j!; z = 10;
v[n_]:= Product[Product[f[k] - f[j], {j,k-1}], {k,2,n}]
Table[v[n], {n,0,z}] (* A203306 *)
Table[v[n+1]/v[n], {n,0,z}] (* A203308 *)
(* Second program *)
Table[Product[(n+1)! - k!, {k,n}], {n,0,10}] (* Vaclav Kotesovec, Jan 25 2019 *)
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from sympy import factorial as f
from operator import mul
from functools import reduce
def v(n):
return 1 if n<2 else reduce(mul, (f(k+1) - f(j) for k in range(1,n) for j in range(1, k+1)))
print([v(n + 1)//v(n) for n in range(16)]) # Indranil Ghosh, Jul 24 2017
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f=factorial; [product(f(n+1) - f(k) for k in range(1,n+1)) for n in range(21)] # G. C. Greubel, Aug 30 2023
A306193
a(n) = Product_{k=0..n} (1 + n!/k!).
Original entry on oeis.org
2, 4, 18, 392, 81250, 225061452, 9854913828914, 7821195286733052688, 128042318400630042200896962, 48734103316428964151516768659332500, 480771737247108575104717059364582638896056402, 135700420467061659867201490569546772642393389614560348824
Offset: 0
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Table[Product[1 + n!/k!, {k, 0, n}], {n, 0, 12}]
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