A122022 -id:A122022 - cp's OEIS frontend

A122050 a(n) = (n-1)*a(n-1) - a(n-4) with a(0)=0, a(1)=1, a(2)=2, a(3)=1.

0, 1, 2, 1, 3, 11, 53, 317, 2216, 17717, 159400, 1593683, 17528297, 210321847, 2734024611, 38274750871, 574103734768, 9185449434441, 156149906360886, 2810660039745077, 53401966651421695, 1068030147578999459, 22428476949252627753, 493423682223518065489

Offset: 0

Roger L. Bagula, Sep 13 2006

nonn

G. C. Greubel, Table of n, a(n) for n = 0..449 [Offset adapted by _Georg Fischer_, Jun 06 2021]

Cf. A122022.

a:=[0,1,2,1];; for n in [5..30] do a[n]:=(n-2)*a[n-1]-a[n-4]; od; a; # G. C. Greubel, Oct 04 2019

I:=[0,1,2,1]; [n le 4 select I[n] else (n-2)*Self(n-1) - Self(n-4): n in [1..30]]; // G. C. Greubel, Oct 04 2019

a := proc (n) option remember;
       if n < 3 then n elif n = 3 then 1 else (n-1)*a(n-1)-a(n-4) end if
     end proc:
seq(a(n), n = 0..30); # G. C. Greubel, Oct 04 2019

a[0]=0; a[1]=1; a[2]=2; a[3]=1; a[n_]:= a[n]= (n-1)*a[n-1] - a[n-4]; Table[a[n], {n, 0, 30}]
RecurrenceTable[{a[0]==0,a[1]==1,a[2]==2,a[3]==1,a[n]==(n-1)a[n-1]- a[n-4]}, a,{n,0,30}] (* Harvey P. Dale, Jul 16 2016 *)
CoefficientList[AsymptoticDSolveValue[{(x^4 + 1)*f[x] - x^2*f'[x] + 3*x^3 - x^2 - x == 0, f[1] == 1}, f[x], {x, 0, 20}], x] (* version >=12, Vaclav Kotesovec, Jun 06 2021 *)

my(m=30, v=concat([0,1,2,1], vector(m-4))); for(n=5, m, v[n] = (n-2)*v[n-1] - v[n-4] ); v \\ G. C. Greubel, Oct 04 2019

def a(n):
    if n<4: return n-1
    elif n==4: return 1
    else: return (n-2)*a(n-1) - a(n-4)
[a(n) for n in (1..30)] # G. C. Greubel, Oct 04 2019

a(n) ~ c * (n-1)!, where c = 0.438972920465828798175530475000702431170711231072281289641... - Vaclav Kotesovec, Jun 06 2021

Offset changed to 0 by Georg Fischer, Jun 06 2021

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

A122049 a(n) = a(n-1) - (n-4)*a(n-4), with a(0)=0, a(1)=1, a(2)=2, a(3)=1.

Original entry on oeis.org

0, 1, 2, 1, 1, 0, -4, -7, -11, -11, 13, 62, 150, 249, 119, -563, -2363, -5600, -7266, 1179, 38987, 134187, 264975, 242574, -537166, -3355093, -9184543, -14763745, -1871761, 82005564, 320803682, 719424797, 771834105, -1606327251, -11230437711, -33532606418

Offset: 0

Roger L. Bagula, Sep 13 2006

sign

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

Cf. A122022.

a:=[0,1,2,1];; for n in [5..30] do a[n]:=a[n-1]-(n-5)*a[n-4]; od; a; # G. C. Greubel, Oct 04 2019

I:=[0,1,2,1]; [n le 4 select I[n] else Self(n-1) - (n-5)*Self(n-4): n in [1..40]]; // G. C. Greubel, Oct 04 2019

a:= proc (n) option remember;
      if n < 3 then n
    elif n = 3 then 1
    else a(n-1) - (n-4)*a(n-4)
      end if
    end proc:
seq(a(n), n = 0..30); # G. C. Greubel, Oct 04 2019

a[0]=0; a[1]=1; a[2]=2; a[3]=1; a[n_]:= a[n]= a[n-1] - (n-4)*a[n-4]; Table[a[n], {n,0,40}]

my(m=40, v=concat([0,1,2,1], vector(m-4))); for(n=5, m, v[n] = v[n-1] - (n-5)*v[n-4] ); v \\ G. C. Greubel, Oct 04 2019

def a(n):
    if n<3: return n
    elif n==3: return 1
    else: return a(n-1) - (n-4)*a(n-4)
[a(n) for n in (0..40)] # G. C. Greubel, Oct 04 2019

a(n) = a(n-1) - (n-4)*a(n-4).

Terms a(31) onward added by G. C. Greubel, Oct 04 2019

cp's OEIS Frontend

A122050 a(n) = (n-1)*a(n-1) - a(n-4) with a(0)=0, a(1)=1, a(2)=2, a(3)=1.

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

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A122049 a(n) = a(n-1) - (n-4)*a(n-4), with a(0)=0, a(1)=1, a(2)=2, a(3)=1.

Views

Author

Keywords

Links

Crossrefs

Programs

GAP

Magma

Maple

Mathematica

PARI

Sage

Formula

Extensions