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
Examples
First 3 rows from A249100: 1; 3, 1; 5, 3, 1; so that the first 3 terms of A249101 are 1, 4, 9.
Crossrefs
Cf. A249100.
Programs
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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 *) -
PARI
{a(n) = if(n<2, n>=0, a(n-1) + (2*n-1)*a(n-2))}; /* Michael Somos, Oct 27 2022 */
Formula
a(n) = a(n-1) + (2*n-1)*a(n-2), a(0) = a(1) = 1. - Michael Somos, Oct 27 2022
Comments