A193661 Q-residue of the triangle A193673, where Q is the triangular array (t(i,j)) given by t(i,j)=1. (See Comments.)

1, 3, 15, 93, 621, 4263, 29595, 206433, 1442841, 10093323, 70633575, 494375973, 3460454661, 24222651183, 169556963955, 1186893964713, 8308243404081, 58157660781843, 407103496332735, 2849724086908653, 19948067446099101

Offset: 0

Author

Clark Kimberling, Aug 02 2011

Keywords

• nonn

Comments

See A193649 for the definition of Q-residue.

Crossrefs

Cf. A193649, A193673.

Programs

Mathematica

q[n_, k_] := 1; r[0] = 1; r[k_] := Sum[q[k - 1, i] r[k - 1 - i], {i, 0, k - 1}]
p[n_, k_] := Coefficient[(1/2) ((x + 3)^n + (x + 1)^n), x, k] (* A193673 *)
v[n_] := Sum[p[n, k] r[n - k], {k, 0, n}]
Table[v[n], {n, 0, 20}]    (* A193661 *)
TableForm[Table[q[i, k], {i, 0, 4}, {k, 0, i}]]
Table[r[k], {k, 0, 8}]  (* 2^k *)
TableForm[Table[p[n, k], {n, 0, 10}, {k, 0, n}]] (* A193673 as a triangle *)
Flatten[%] (* A193673 as a sequence *)

Formula

Conjecture: G.f.: ( -1+8*x-13*x^2 ) / ( (x-1)*(3*x-1)*(7*x-1) ). - R. J. Mathar, Feb 19 2015