cp's OEIS Frontend

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

%I A249101 #17 Oct 28 2022 09:58:01
%S A249101 1,4,9,37,118,525,2059,9934,44937,233683,1177360,6552069,35986069,
%T A249101 212891932,1256487933,7856137825,49320239614,324285063489,
%U A249101 2149133929207,14796251405278,102910742502765,739149552929719,5370132965554144,40110161953250937
%N A249101 p(n,1), where p(n,x) is defined in Comments; sum of numbers in row n of the array at A249100.
%C A249101 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.
%F A249101 a(n) = a(n-1) + (2*n-1)*a(n-2), a(0) = a(1) = 1. - _Michael Somos_, Oct 27 2022
%e A249101 First 3 rows from A249100:
%e A249101   1;
%e A249101   3,  1;
%e A249101   5,  3,  1;
%e A249101 so that the first 3 terms of A249101 are 1, 4, 9.
%t A249101 z = 11; p[n_, x_] := x + (2 n - 1)/p[n-1,x]; p[1,x_] = 1;
%t A249101 t = Table[Factor[p[n,x]], {n, 1, z}]
%t A249101 u = Numerator[t]; v = u /. x -> 1  (* A249101 *)
%t 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 *)
%o A249101 (PARI) {a(n) = if(n<2, n>=0, a(n-1) + (2*n-1)*a(n-2))}; /* _Michael Somos_, Oct 27 2022 */
%Y A249101 Cf. A249100.
%K A249101 nonn,easy
%O A249101 1,2
%A A249101 _Clark Kimberling_, Oct 21 2014