A275825 Third-order sequence with non-constant coefficients: a(n) = (n-3)*a(n-1) + (n-1)*a(n-3); a(0) = a(1) = a(2) = 1.

1, 1, 1, 2, 5, 14, 52, 238, 1288, 8144, 59150, 486080, 4464304, 45352840, 505200280, 6124903616, 80304039608, 1132339758992, 17089219746352, 274872988654576, 4694355262548640, 84840179120802560, 1617735736056994736, 32457990536915964800, 683569125395013719680

Offset: 0

Author

Christopher C. Capobianco, Sep 13 2016

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..450

Crossrefs

Cf. A000930, A000931.

Programs

C

int seq(int n) {int v = 1; if(n <= 2) {v = 1;} else {v = (n-3)*seq(n-1) + (n-1)*seq(n-3);}return v;}

Maple

f:= gfun:-rectoproc({a(n) = (n-3)*a(n-1) + (n-1)*a(n-3), a(0) = 1,a(1) = 1, a(2) = 1}, a(n), remember):
map(f, [$0..30]); # Robert Israel, Nov 08 2016

Mathematica

RecurrenceTable[{a[n+1]==(n-2)*a[n]+n*a[n-2],a[0]==1,a[1]==1,a[2]==1},a,{n,0,15}]
nxt[{n_,a_,b_,c_}]:={n+1,b,c,c(n-2)+n*a}; NestList[nxt,{2,1,1,1},30][[;;,2]] (* Harvey P. Dale, Jul 22 2025 *)

Formula

a(n) ~ c * n^(n-5/2) / exp(n), where c = 35.33624296996624315241349866820530476... . - Vaclav Kotesovec, Oct 04 2016