A249101 p(n,1), where p(n,x) is defined in Comments; sum of numbers in row n of the array at A249100.

1, 4, 9, 37, 118, 525, 2059, 9934, 44937, 233683, 1177360, 6552069, 35986069, 212891932, 1256487933, 7856137825, 49320239614, 324285063489, 2149133929207, 14796251405278, 102910742502765, 739149552929719, 5370132965554144, 40110161953250937

Offset

1,2

Comments

The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = x + (2*n - 1)/f(n-1,x), where f(1,x) = 1.

Links

Table of n, a(n) for n=1..24.

Formula

a(n) = a(n-1) + (2*n-1)*a(n-2), a(0) = a(1) = 1. - Michael Somos, Oct 27 2022

Example

First 3 rows from A249100:
  1;
  3,  1;
  5,  3,  1;
so that the first 3 terms of A249101 are 1, 4, 9.

Mathematica

z = 11; p[n_, x_] := x + (2 n - 1)/p[n-1, x]; p[1, x_] = 1;
t = Table[Factor[p[n, x]], {n, 1, z}]
u = Numerator[t]; v = u /. x -> 1  (* A249101 *)
a[ n_] := (a[n] = If[n<2, Boole[n>=0], a[n-1] + (2*n-1)*a[n-2]]); (* Michael Somos, Oct 27 2022 *)

Prog

(PARI) {a(n) = if(n<2, n>=0, a(n-1) + (2*n-1)*a(n-2))}; /* Michael Somos, Oct 27 2022 */

Crossrefs

Cf. A249100.

Sequence in context: A055872 A066924 A251689 * A289157 A149146 A149147

Adjacent sequences: A249098 A249099 A249100 * A249102 A249103 A249104

Keyword

nonn,easy

Author

Clark Kimberling, Oct 21 2014

Status

approved