A193660 Q-residue of the triangle A038207 of coefficients of (x+2)^n, where Q is the triangle given by t(i,j)=1 for 0<=i<=j. (See Comments.)

1, 2, 5, 22, 201, 3690, 131149, 9004286, 1204317329, 316525415890, 164556516205461, 169974659148800742, 349799994417738642265, 1436618749673583674658362, 11785996128174350460348176861, 193254862258295280115072223316430

Offset: 0

Author

Clark Kimberling, Aug 02 2011

Keywords

• nonn

Comments

For the definition of Q-residue, see A193649.

Crossrefs

Cf. A038207, A126443, A193649.

Programs

Mathematica

q[n_, k_] := Coefficient[(x + 2)^n, x, k]; (* A038207 *)
r[0] = 1; r[k_] := Sum[q[k - 1, i] r[k - 1 - i], {i, 0, k - 1}]
p[n_, k_] := 1
v[n_] := Sum[p[n, k] r[n - k], {k, 0, n}]
Table[v[n], {n, 0, 16}]    (* A038207 *)
TableForm[Table[q[i, k], {i, 0, 4}, {k, 0, i}]]
Table[r[k], {k, 0, 8}]  (* A126443 *)
TableForm[Table[p[n, k], {n, 0, 4}, {k, 0, n}]]