A122021 -id:A122021 - cp's OEIS frontend

A122048 a(n) = (n-2)*a(n-2) - a(n-3), with a(0)=0, a(1)=1, a(2)=2.

0, 1, 2, 1, 3, 1, 11, 2, 65, 3, 518, -38, 5177, -936, 62162, -17345, 871204, -322337, 13956609, -6350933, 251541299, -134624336, 5037176913, -3078652355, 110952516422, -75846181078, 2665939046483, -2007107043372, 69390261389636, -56857829217527, 1944934425953180

Offset: 0

Roger L. Bagula, Sep 13 2006

sign

G. C. Greubel, Table of n, a(n) for n = 0..800

Cf. A122021.

a:=[0,1,2,1];; for n in [5..35] do a[n]:=(n-3)*a[n-2]-a[n-3]; od; a; # G. C. Greubel, Oct 04 2019

I:=[0,1,2,1]; [n le 4 select I[n] else (n-3)*Self(n-2) - Self(n-3): n in [1..35]]; // G. C. Greubel, Oct 04 2019

a:= proc (n) option remember;
      if n < 3 then n
    elif n = 3 then 1
    else (n-2)*a(n-2) - a(n-3)
      end if
    end proc:
seq(a(n), n = 0..35); # G. C. Greubel, Oct 04 2019

a[0]=0; a[1]=1; a[2]=2; a[n_]:= a[n]= (n-2)*a[n-2] - a[n-3]; Table[a[n], {n, 0, 35}]

my(m=35, v=concat([0,1,2,1], vector(m-4))); for(n=5, m, v[n] = (n-3)*v[n-2] - v[n-3] ); v \\ G. C. Greubel, Oct 04 2019

def a(n):
    if n<3: return n
    elif n==3: return 1
    else: return (n-2)*a(n-2) - a(n-3)
[a(n) for n in (0..35)] # G. C. Greubel, Oct 04 2019

a(n) = (n-2)*a(n-2) - a(n-3).

Offset changed by G. C. Greubel, Oct 04 2019

A122031 a(n) = a(n - 1) + (n - 1)*a(n - 2).

Original entry on oeis.org

1, 2, 3, 7, 16, 44, 124, 388, 1256, 4360, 15664, 59264, 231568, 942736, 3953120, 17151424, 76448224, 350871008, 1650490816, 7966168960, 39325494464, 198648873664, 1024484257408, 5394759478016, 28957897398400

Offset: 0

Roger L. Bagula, Sep 13 2006

nonn

Equals the eigensequence of an infinite lower triangular matrix with (1, 1, 1, ...) in the main diagaonal, (1, 1, 2, 3, 4, 5, ...) in the subdiagonal and the rest zeros. - Gary W. Adamson, Apr 13 2009

G. C. Greubel, Table of n, a(n) for n = 0..795

Cf. A000898, A062267, A121966, A122021, A122022.

a[0] = 1; a[1] = 2; a[n_] := a[n] = a[n - 1] + (n - 1)*a[n - 2] Table[a[n], {n, 0, 30}]
Table[n!*SeriesCoefficient[1/2*Exp[x+x^2/2]*(2-Sqrt[2*E*Pi]*Erf[1/Sqrt[2]]+Sqrt[2*E*Pi]*Erf[(1+x)/Sqrt[2]]),{x,0,n}],{n,0,20}] (* Vaclav Kotesovec after Paul Abbott, Dec 27 2012 *)
RecurrenceTable[{a[0]==1,a[1]==2,a[n]==a[n-1]+(n-1)a[n-2]},a,{n,30}] (* Harvey P. Dale, Feb 21 2015 *)

E.g.f.: (1/2)*exp(x + x^2/2)*(2 - sqrt(2*exp(1)*Pi)*erf(1/sqrt(2)) + sqrt(2*exp(1)*Pi)*erf((1+x)/sqrt(2))). - Paul Abbott (paul(AT) physics.uwa.edu.au)

a(n) ~ (1/sqrt(2) + sqrt(Pi)/2*exp(1/2) * (1 - erf(1/sqrt(2)))) * n^(n/2)*exp(sqrt(n) - n/2 - 1/4) * (1+7/(24*sqrt(n))). - Vaclav Kotesovec, Dec 27 2012

Edited by N. J. A. Sloane, Sep 17 2006

Offset corrected by Vaclav Kotesovec, Dec 27 2012

A122044 a(n) = a(n-2) - (n-3)*a(n-3), with a(0)=0, a(1)=1, a(2)=2.

Original entry on oeis.org

0, 1, 2, 1, 1, -3, -2, -7, 13, 5, 62, -99, 17, -719, 1106, -923, 10453, -16407, 24298, -183655, 303217, -621019, 3792662, -6685359, 16834061, -90123923, 170597318, -494141387, 2423695393, -4929671655, 15765512842, -72793142659, 158725990837, -545758527919, 2415313413266

Offset: 0

Roger L. Bagula, Sep 13 2006

G. C. Greubel, Table of n, a(n) for n = 0..1000

Cf. A122021, A122048, A122050.

a:=[0,1,2];; for n in [4..35] do a[n]:=a[n-2]-(n-4)*a[n-3]; od; a; # G. C. Greubel, Oct 04 2019

I:=[0,1,2]; [n le 3 select I[n] else Self(n-2) - (n-4)*Self(n-3): n in [1..35]]; // G. C. Greubel, Oct 04 2019

a:= proc(n) option remember;
      if n < 3 then n
    else a(n-2)-(n-3)*a(n-3)
      fi;
    end proc:
seq(a(n), n = 0..35); # G. C. Greubel, Oct 04 2019

a[0]=0; a[1]=1; a[2]=2; a[n_]:= a[n]= a[n-2] - (n-3)*a[n-3]; Table[a[n], {n, 0, 35}]

my(m=35, v=concat([0,1,2], vector(m-3))); for(n=4, m, v[n] = v[n-2] - (n-4)*v[n-3] ); v \\ G. C. Greubel, Oct 04 2019

def a(n):
    if n<3: return n
    else: return a(n-2) - (n-3)*a(n-3)
[a(n) for n in (0..35)] # G. C. Greubel, Oct 04 2019

a(n) = a(n-2) - (n-3)*a(n-3), with a(0)=0, a(1)=1, a(2)=2. - G. C. Greubel, Oct 04 2019

Edited by N. J. A. Sloane, Sep 17 2006

More terms from Max Alekseyev, Sep 13 2009

cp's OEIS Frontend

A122048 a(n) = (n-2)*a(n-2) - a(n-3), with a(0)=0, a(1)=1, a(2)=2.

Views

Author

Keywords

Links

Crossrefs

Programs

GAP

Magma

Maple

Mathematica

PARI

Sage

Formula

Extensions

A122031 a(n) = a(n - 1) + (n - 1)*a(n - 2).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A122044 a(n) = a(n-2) - (n-3)*a(n-3), with a(0)=0, a(1)=1, a(2)=2.

Views

Author

Keywords

Links

Crossrefs

Programs

GAP

Magma

Maple

Mathematica

PARI

Sage

Formula

Extensions