A203748
Vandermonde sequence using x^2 + xy + y^2 applied to (0,1,1,2,2,...,floor(n/2)).
Original entry on oeis.org
1, 1, 3, 588, 1382976, 759365845056, 11257740654368225472, 85256857822344357223236943872, 30991931452969951465382132459004342829056, 10117962915393557751514211466029580457669394910570086400
Offset: 1
-
f[j_] := Floor[j/2]; z = 15;
u := Product[f[j]^2 + f[j] f[k] + f[k]^2, {j, 1, k - 1}]
v[n_] := Product[u, {k, 2, n}]
Table[v[n], {n, 1, z}] (* A203748 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203749 *)
Table[Sqrt[v[n + 1]/v[n]], {n, 1, z}]
Table[Sqrt[v[2 n]/v[2 n - 1]], {n, 1, z}] (* A203750 *)
Table[Sqrt[v[2 n + 1]/(3 v[2 n])],
{n, 1, z}] (* A203751 *)
%/%% (* A000027 *)
A203774
Square root of v(2n)/v(2n-1), where v=A203773.
Original entry on oeis.org
1, 10, 390, 34000, 5255380, 1267531200, 439881715000, 207679463680000, 128024359806330000, 99861207456574720000, 96148662977402249500000, 112000625784958629888000000, 155250403381700932802965000000
Offset: 1
Triangle ( f(n)/(f(k)*f(n-k)) )0<=k<=n begins
1
1 1
1 10 1
1 390 390 1
1 34000 1326000 34000 1
- _Peter Bala_, Sep 21 2013
Original entry on oeis.org
1, 3, 196, 2352, 549081, 14825187, 7573176576, 363512475648, 326470872935025, 24485315470126875, 34169385402567926784, 3690293623477336092672, 7392237545597804070571449, 1086658919202877198374003003
Offset: 1
-
f[j_] := Floor[j/2]; z = 15;
u := Product[f[j]^2 + f[j] f[k] + f[k]^2, {j, 1, k - 1}]
v[n_] := Product[u, {k, 2, n}]
Table[v[n], {n, 1, z}] (* A203748 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203749 *)
Table[Sqrt[v[n + 1]/v[n]], {n, 1, z}]
Table[Sqrt[v[2 n]/v[2 n - 1]], {n, 1, z}] (* A203750 *)
Table[Sqrt[v[2 n + 1]/(3 v[2 n])],
{n, 1, z}] (* A203751 *)
%/%% (* A000027 *)
Showing 1-3 of 3 results.
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