A203773
Vandermonde sequence using x^2 + y^2 applied to (0,1,1,2,2,...,floor(n/2)).
Original entry on oeis.org
1, 1, 2, 200, 160000, 24336000000, 66627100800000000, 77020928524800000000000000, 2849158187989401600000000000000000000, 78690953969671659336819671040000000000000000000000
Offset: 1
-
f[j_] := Floor[j/2]; z = 20;
u := Product[f[j]^2 + f[k]^2, {j, 1, k - 1}]
v[n_] := Product[u, {k, 2, n}]
Table[v[n], {n, 1, z}] (* A203773 *)
Table[v[n + 1]/v[n], {n, 1, z}]
Table[Sqrt[v[n + 1]/v[n]], {n, 1, z}]
Table[Sqrt[v[2 n]/v[2 n - 1]], {n, 1, z}] (* A203774 *)
Table[Sqrt[v[2 n + 1]/(2 v[2 n])],
{n, 1, z}] (* A203775 *)
%/%% (* A000027 *)
A203750
Square root of v(2n)/v(2n-1), where v=A203748.
Original entry on oeis.org
1, 14, 741, 87024, 18068505, 5845458528, 2718866959893, 1719570636306432, 1419543579377755377, 1482454643117692608000, 1910657530214126188243749, 2978927846824451394372304896, 5526241720077994999033052180169
Offset: 1
Triangle ( f(n)/(f(k)*f(n-k)) ), 0 <= k <= n, begins
1;
1, 1;
1, 14, 1;
1, 741, 741, 1;
1, 87024, 4606056, 87024, 1;
... - _Peter Bala_, Sep 21 2013
Original entry on oeis.org
1, 2, 100, 800, 152100, 2737800, 1156000000, 36992000000, 27619018944400, 1380950947220000, 1606635342973440000, 115677744694087680000, 193495923191341225000000, 18962600472751440050000000
Offset: 1
-
f[j_] := Floor[j/2]; z = 20;
u := Product[f[j]^2 + f[k]^2, {j, 1, k - 1}]
v[n_] := Product[u, {k, 2, n}]
Table[v[n], {n, 1, z}] (* A203773 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A202945 *)
Table[Sqrt[v[n + 1]/v[n]], {n, 1, z}]
Table[Sqrt[v[2 n]/v[2 n - 1]], {n, 1, z}] (* A203774 *)
Table[Sqrt[v[2 n + 1]/(2 v[2 n])],
{n, 1, z}] (* A203775 *)
%/%% (* A000027 *)
Showing 1-3 of 3 results.
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