A256710 a(n) = (2*n-3)*a(n-1) - 2*a(n-2), a(0)=0, a(1)=1.

0, 1, 1, 1, 3, 19, 165, 1777, 22771, 338011, 5700645, 107636233, 2248959603, 51510798403, 1283272040869, 34545323506657, 999247837611315, 30907592318937451, 1017952050849713253, 35566506595102088953, 1313924839917077864755, 51171935743575832547539

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..400

Formula

E.g.f.: (1/sqrt(2))*sin(sqrt(2)*(1-sqrt(1-2*x))).

a(n) ~ cos(sqrt(2)) * 2^(n - 1/2) * n^(n-1) / exp(n). - Vaclav Kotesovec, Mar 13 2020

Maple

a:= proc(n) option remember; `if`(n<2, n,
      (2*n-3)*a(n-1)-2*a(n-2))
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Apr 10 2015

Mathematica

RecurrenceTable[{a[0]==a[1]==1, a[n+2]==(2n+1)a[n+1]-2a[n]}, a, {n, 20}]
a[n_]:=(2n-3)*a[n-1]-2a[n-2]; a[0]=0; a[1]=1; Array[a, 21, 0] (* or *)
Range[0, 20]! CoefficientList[ Simplify[ Series[ Sin[ Sqrt[2]*(1 - Sqrt[1 - 2 x])]/Sqrt[2], {x, 0, 20}]], x]
(* Robert G. Wilson v, Apr 08 2015 *)
nxt[{n_, a_, b_}]:={n+1, b, b*(2n-1)-2a}; NestList[nxt, {1, 0, 1}, 30][[All, 2]] (* Harvey P. Dale, Jun 21 2020 *)

Prog

(Magma) [0] cat [n le 2 select 1 else (2*n-3)*Self(n-1)-2*Self(n-2): n in [1..50]]; // Vincenzo Librandi, Apr 09 2015

Crossrefs

Sequence in context: A136474 A337818 A183069 * A215093 A201123 A260700

Adjacent sequences: A256707 A256708 A256709 * A256711 A256712 A256713

Keyword

nonn,easy

Author

G. C. Greubel, Apr 08 2015

Status

approved