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MATHEMATICA
| Series[ AiryAi[ x ], {x, 0, 30} ]
a[ n_] := If[ n<0, 0, (n + Quotient[ n, 2])! / Product[ 3 k + 1 + Mod[n, 2], {k, 0, Quotient[ n, 2] - 1}]] (* Michael Somos, Oct 14 2011 *)
(* Next, A014402 generated in via Vandermonde determinants based on A007494 *)
f[j_] := j + Floor[(j + 1)/2]; z = 18;
v[n_] := Product[Product[f[k] - f[j], {j, 1, k - 1}], {k, 2, n}]
d[n_] := Product[(i - 1)!, {i, 1, n}]
Table[v[n], {n, 1, z}] (* A203433 *)
Table[v[n + 1]/v[n], {n, 1, z - 1}] (* A014402 *)
Table[v[n]/d[n], {n, 1, 20}] (* A203434 *)
(* Clark Kimberling, Jan 02 2012 *)
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