This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A193895 Triangular array:  the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{(k+1)*x^(n-k) : 0<=k<=n} and q(n,x)=sum{(k+1)*x^k : 0<=k<=n}. 2
 1, 2, 1, 6, 6, 3, 12, 15, 12, 6, 20, 28, 27, 20, 10, 30, 45, 48, 42, 30, 15, 42, 66, 75, 72, 60, 42, 21, 56, 91, 108, 110, 100, 81, 56, 28, 72, 120, 147, 156, 150, 132, 105, 72, 36, 90, 153, 192, 210, 210, 195, 168, 132, 90, 45, 110, 190, 243, 272, 280, 270 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS See A193722 for the definition of fusion of P by Q (two sequences of polynomials or triangular arrays). ... First six rows of P, the coefficients of (p(n,x)): 1 1...2 1...2...3 1...2...3...4 1...2...3...4...5 ... First six rows of Q, the coefficients of (q(n,x)): 1 2...1 3...2...1 4...3...2...1 5...4..3...2..1 LINKS EXAMPLE First six rows of A193895: 1 2....1 6....6....3 12...15...12...6 20...28...27...20...10 30...45...48...42...30...15 MATHEMATICA z = 9; p[n_, x_] := x*p[n - 1, x] + n + 1 (* #6 *)  ; p[0, x_] := 1; q[n_, x_] := (n + 1)*x^n + q[n - 1, x] (* #7 *); q[0, x_] := 1; t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0; w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1 g[n_] := CoefficientList[w[n, x], {x}] TableForm[Table[Reverse[g[n]], {n, -1, z}]] Flatten[Table[Reverse[g[n]], {n, -1, z}]]  (* A193895 *) TableForm[Table[g[n], {n, -1, z}]] Flatten[Table[g[n], {n, -1, z}]]  (* A193896 *) CROSSREFS Sequence in context: A260885 A075181 A052121 * A193561 A117965 A111646 Adjacent sequences:  A193892 A193893 A193894 * A193896 A193897 A193898 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 08 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 26 12:27 EDT 2019. Contains 321497 sequences. (Running on oeis4.)