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 A193654 Q-residue of the triangle p(n,k)=floor((n+1)/(n+k+2)/2), 0<=k<=n, where Q is the triangular array (t(i,j)) given by t(i,j)=1.  (See Comments.) 2
 1, 7, 28, 94, 275, 765, 2002, 5116, 12625, 30715, 73040, 172026, 398671, 917497, 2086222, 4718584, 10573133, 23592951, 52254028 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For the definition of Q-residue, see A193649. LINKS FORMULA Conjecture: G.f.: ( -1-2*x+4*x^2+4*x^3-8*x^5 ) / ( (1+x)*(2*x+1)*(x-1)^2*(2*x-1)^3 ). - R. J. Mathar, Feb 19 2015 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_] := Floor[(n + 1) (n + k + 2)/2] v[n_] := Sum[p[n, k] r[n - k], {k, 0, n}] Table[v[n], {n, 0, 16}]    (* A193654 *) 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, 4}, {k, 0, n}]] CROSSREFS Cf. A193649, A193655. Sequence in context: A224153 A276236 A022572 * A241400 A219411 A224404 Adjacent sequences:  A193651 A193652 A193653 * A193655 A193656 A193657 KEYWORD nonn AUTHOR Clark Kimberling, Aug 02 2011 STATUS approved

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Last modified May 6 08:08 EDT 2021. Contains 343580 sequences. (Running on oeis4.)