This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A247376 Triangular array:  row n gives the coefficients of the polynomial p(n,x) defined in Comments. 1
 1, 2, 2, 3, 5, 5, 15, 8, 8, 35, 33, 13, 80, 131, 48, 21, 171, 409, 279, 34, 355, 1180, 1375, 384, 55, 715, 3128, 5335, 2895, 89, 1410, 7858, 18510, 17029, 3840, 144, 2730, 18851, 58253, 78609, 35685, 233, 5208, 43629, 171059, 317758, 243873, 46080, 377, 9810 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = 1 + (2*x + 1)/f(n-1,x), where f(0,x) = 1. (Sum of numbers in row n) = A059480(n+1) for n >= 0. (Column 1) is essentially A000045 (Fibonacci numbers). LINKS Clark Kimberling, Rows 0..100, flattened FORMULA f(0,x) = 1/1, so that p(0,x) = 1 f(1,x) = (2 + 2 x)/1, so that p(1,x) = 2 + 2 x; f(2,x) = (3 + 5 x)/(2 + 2 x), so that p(2,x) = 3 + 5 x. First 6 rows of the triangle of coefficients: 1 2    2 3    5 5    15    8 8    35    33 13   80    131   48 MATHEMATICA z = 15; f[x_, n_] := 1 + (2 x + 1)/f[x, n - 1]; f[x_, 1] = 1; t = Table[Factor[f[x, n]], {n, 1, z}] u = Numerator[t] TableForm[Table[CoefficientList[u[[n]], x], {n, 1, z}]] (* A247376 array *) Flatten[CoefficientList[u, x]] (* A247376 sequence *) PROG (PARI) rown(n) = if (n==0, 1, 1 + (2*x+1)/rown(n-1)); tabl(nn) = for (n=0, nn, print(Vecrev(numerator(rown(n))))); \\ Michel Marcus, Oct 28 2014 CROSSREFS Cf. A059480, A000045. Sequence in context: A035537 A285407 A292802 * A101779 A169891 A137756 Adjacent sequences:  A247373 A247374 A247375 * A247377 A247378 A247379 KEYWORD nonn,tabf,easy AUTHOR Clark Kimberling, Oct 23 2014 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 June 25 05:41 EDT 2019. Contains 324346 sequences. (Running on oeis4.)