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MATHEMATICA
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q[n_, k_] := (k + 1) (n + 1); (* A075362 *)
r[0] = 1; r[k_] := Sum[q[k - 1, i] r[k - 1 - i], {i, 0, k - 1}];
p[n_, k_] := (k + 1) (n + 1); (* A075362 *)
v[n_] := Sum[p[n, k] r[n - k], {k, 0, n}]
Table[v[n], {n, 0, 20}] (* A193665 *)
TableForm[Table[q[i, k], {i, 0, 4}, {k, 0, i}]]
Table[r[k], {k, 0, 8}] (* A193665 *)
TableForm[Table[p[n, k], {n, 0, 4}, {k, 0, n}]]
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