The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A193919 Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers), and q(n,x)=(x+1)^n. 2
 1, 1, 1, 1, 3, 2, 2, 7, 9, 4, 3, 14, 25, 21, 7, 5, 28, 64, 75, 46, 12, 8, 53, 148, 224, 195, 94, 20, 13, 99, 326, 603, 679, 468, 185, 33, 21, 181, 687, 1502, 2073, 1855, 1056, 353, 54, 34, 327, 1405, 3543, 5786, 6357, 4711, 2280, 659, 88, 55, 584, 2802, 8005 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays. LINKS Table of n, a(n) for n=0..58. EXAMPLE First six rows: 1 1...1 1...3....2 2...7....9....4 3...14...25...21...7 5...28...64...75...46...12 MATHEMATICA p[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}]; q[n_, x_] := (x + 1)^n; 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}]] (* A193919 *) TableForm[Table[g[n], {n, -1, z}]] Flatten[Table[g[n], {n, -1, z}]] (* A193920 *) CROSSREFS Cf. A193722, A193920. Sequence in context: A020835 A244639 A352673 * A055674 A210612 A266275 Adjacent sequences: A193916 A193917 A193918 * A193920 A193921 A193922 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 09 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 2 05:08 EST 2024. Contains 370460 sequences. (Running on oeis4.)