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A081405   a(n) = (n+1)*a(n-2) with a(0) = a(1) = 1. 6
1, 1, 3, 4, 15, 24, 105, 192, 945, 1920, 10395, 23040, 135135, 322560, 2027025, 5160960, 34459425, 92897280, 654729075, 1857945600, 13749310575, 40874803200, 316234143225, 980995276800, 7905853580625, 25505877196800, 213458046676875 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A001147 and A002866 combined.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..790

FORMULA

a(0)=a(1)=1; a(2n) = A001147(2*n-2) odd terms, double factorial numbers; a(2n-1) = A002866(n) = 2^(n-1)*n!

0 = a(n)*(a(n+1) - a(n+3)) + a(n+1)*a(n+2) if n>=0. - Michael Somos, Jan 24 2014

a(n) = (n-1)-st term of column 1 of the array at A249159, for n >= 0. - Clark Kimberling, Oct 23 2014

EXAMPLE

G.f. = 1 + x + 3*x^2 + 4*x^3 + 15*x^4 + 24*x^5 + 105*x^6 + 192*x^7 + ...

MAPLE

a[0]:=1:a[1]:=1:for n from 2 to 50 do a[n]:=(a[n-2]*(n+1)^2) od: seq(sqrt(a[n]), n=0..26); # Zerinvary Lajos, Mar 04 2008

MATHEMATICA

f[n_]:= (n+1)*f[n-2]; f[0] = 1; f[1] = 1; Table[f[n], {n, 1, 30}]

a[ n_]:= If[ n < 0, 0, If[OddQ[n], 2^((n-1)/2) ((n+1)/2)!, (n+1)!!]]; (* Michael Somos, Jan 24 2014 *)

PROG

(PARI) {a(n) = if( n<2, n>=0, (n+1) * a(n-2))}; /* Michael Somos, Jan 24 2014 */

(PARI) {a(n) = if( n<0, 0, if( n%2, 2^(n\2) * (n\2 + 1)!, (n+1)! / (2^(n\2) * (n\2)!)))}; /* Michael Somos, Jan 24 2014 */

(MAGMA) [n le 1 select 1 else (n+1)*Self(n-1): n in [0..30]]; // Vincenzo Librandi, Oct 26 2014

(Sage)

def a(n):

    if n<2: return 1

    else: return (n+1)*a(n-2)

[a(n) for n in (0..30)] # G. C. Greubel, Aug 24 2019

(GAP)

a:= function(n)

    if n<2 then return 1;

    else return (n+1)*a(n-2);

    fi;

  end;

List([0..30], n-> a(n) ); # G. C. Greubel, Aug 24 2019

CROSSREFS

Cf. A000142, A001147, A002866.

Sequence in context: A286645 A290863 A086826 * A167367 A024858 A293047

Adjacent sequences:  A081402 A081403 A081404 * A081406 A081407 A081408

KEYWORD

nonn

AUTHOR

Labos Elemer, Apr 01 2003

STATUS

approved

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Last modified June 21 10:09 EDT 2021. Contains 345360 sequences. (Running on oeis4.)