A237622 Interpolation polynomial through n points (0,1), (1,1), ..., (n-2,1) and (n-1,n) evaluated at 2n, a(0)=1.
1, 1, 5, 31, 169, 841, 3961, 18019, 80081, 350065, 1511641, 6466461, 27457585, 115892401, 486748081, 2035917451, 8485840801, 35263382881, 146157442201, 604404010981, 2494365759601, 10275832148401, 42264944401681, 173588164506901, 712027089322849
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
Programs
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Maple
a:= proc(n) option remember; `if`(n<3, [1, 1, 5][n+1], (n*(15*n^3-44*n^2+43*n-18) *a(n-1) -2*(n-1)*(2*n-3)*(3*n^2-n+2) *a(n-2))/ ((n-2)*(n+1)*(3*n^2-7*n+6))) end: seq(a(n), n=0..30); -
Mathematica
a[n_] := Module[{m}, If[n == 0, 1, InterpolatingPolynomial[Table[{k, If[k == n-1, n, 1]}, {k, 0, n-1}], m] /. m -> 2n]]; a /@ Range[0, 30] (* Jean-François Alcover, Dec 22 2020 *)
Formula
E.g.f.: exp(x)+2*exp(2*x)*(BesselI(1,2*x)*(x-1)+x*BesselI(0,2*x)).
a(n) ~ sqrt(n)*4^n/sqrt(Pi). - Vaclav Kotesovec, Feb 14 2014