A193665 Q-residue of A075392, where Q=A075392. (See Comments.)

1, 6, 33, 208, 1505, 12330, 112973, 1145568, 12742389, 154308350, 2021296189, 28480485024, 429565218277, 6905903216562, 117891260108985, 2129869055824000, 40600135597843817, 814383095809997142, 17147155400516728601, 378137512431282658800

Offset: 0

Author

Clark Kimberling, Aug 02 2011

Keywords

• nonn

Comments

The definition of Q-residue is given at A193649.

Crossrefs

Cf. A075362, A193649.

Programs

Mathematica

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}]]

Formula

Conjecture: a(n) +(-n-4)*a(n-1) +(n+1)*a(n-2) -a(n-3)=0. - R. J. Mathar, Feb 19 2015