A324402
a(n) = Product_{i=1..n, j=1..n} (2*i + j).
Original entry on oeis.org
1, 3, 360, 6350400, 36212520960000, 117563342374788710400000, 337905477880065368190647009280000000, 1234818479230749311108497004714406224855040000000000, 7795494015765035913020359514023640290443493305037073940480000000000000
Offset: 0
-
f:= n -> mul((2*i+n)!/(2*i)!,i=1..n):
map(f, [$0..10]); # Robert Israel, Feb 27 2019
-
Table[Product[2*i+j, {i, 1, n}, {j, 1, n}], {n, 1, 10}]
A227143
Hankel determinants of order n of A225439(n): a(n)=det[A225439(i+j-2)], i,j=0..n, n>=0.
Original entry on oeis.org
1, 1, 12, 567, 122472, 126660105, 640190834712, 15987980408180508, 1985745116187976972608, 1231754497376142871049675940, 3826847477714307687323719819461000, 59670909707615018862830973519922857945375
Offset: 0
-
with(LinearAlgebra):
A225439 := proc(n) add(binomial(k,n-k)*3^(k)*(-1)^(n-k)*binomial(n+k-1,n-1), k=0..n) end:
hank0:= (i, j)-> A225439(i+j-2):
a:= proc(n) Determinant(Matrix(n,n,hank0)) end:
seq(a(n), n=0..10);
-
A225439[n_] := Sum[Binomial[k, n-k]*3^k*(-1)^(n-k)*Binomial[n+k-1, n-1], {k, 0, n}]; a[n_] := Det[Table[A225439[i+j-2], {i, n}, {j, n}]]; a[0] = 1; Table[ a[n], {n, 0, 11}] (* Jean-François Alcover, Nov 07 2016 *)
A227379
Hankel determinants of order n of A225439(n): a(n) = det[A225439(i+j-1)], i,j=0..n, n>=0.
Original entry on oeis.org
1, 3, 45, 3402, 1299078, 2507870079, 24487299427734, 1209640056157393380, 302358334494179897593596, 382459771435292361460924379370, 2448391839613471201062299337071282925
Offset: 0
-
with(LinearAlgebra):
A225439 := proc(n) add(binomial(k, n-k)*3^(k)*(-1)^(n-k)*binomial(n+k-1, n-1), k=0..n) end:
hank1:= (i, j)-> A225439(i+j-1):
a:= proc(n) Determinant(Matrix(n, n, hank1)) end:
seq(a(n), n=0..10);
-
A225439[n_] := Sum[Binomial[k, n-k]*3^k*(-1)^(n-k)*Binomial[n+k-1, n-1], {k, 0, n}]; a[n_] := Det[Table[A225439[i+j-1], {i, n}, {j, n}]]; a[0] = 1; Table[ a[n], {n, 0, 11}] (* Vaclav Kotesovec, Feb 24 2019, after Jean-François Alcover *)
Showing 1-3 of 3 results.