A193659 - OEIS

A193659

Q-residue of the triangle A094727, where Q=Pascal's triangle. (See Comments.)

1, 2, 8, 43, 265, 1832, 14160, 121771, 1157557, 12080436, 137505288, 1696841395, 22578385961, 322377704664, 4917809053032, 79840791037379, 1374705370985669, 25024307510421060, 480230285880218992

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OFFSET

0,2

COMMENTS

For the definition of Q-residue, see A193649.

LINKS

Table of n, a(n) for n=0..18.

FORMULA

Conjecture: a(n) +(-n-5)*a(n-1) +2*(2*n+1)*a(n-2) +(-5*n+8)*a(n-3) +2*(n-3)

*a(n-4)=0. - R. J. Mathar, Feb 19 2015

MATHEMATICA

q[n_, k_] := n + k + 1; (* A094727 *)

r[0] = 1; r[k_] := Sum[q[k - 1, i] r[k - 1 - i], {i, 0, k - 1}]

p[n_, k_] := n!/(k! (n - k)!); (* Pascal's triangle *)

v[n_] := Sum[p[n, k] r[n - k], {k, 0, n}]

Table[v[n], {n, 0, 18}] (* A193659 *)

TableForm[Table[q[i, k], {i, 0, 4}, {k, 0, i}]]

Table[r[k], {k, 0, 8}] (* A193668 *)

TableForm[Table[p[n, k], {n, 0, 4}, {k, 0, n}]]

CROSSREFS

Cf. A193668, A094727, A193649.

Sequence in context: A050637 A349145 A188174 * A020023 A027836 A326561

Adjacent sequences: A193656 A193657 A193658 * A193660 A193661 A193662

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 02 2011

STATUS

approved