A019465 Multiply by 1, add 1, multiply by 2, add 2, etc., start with 2.

2, 2, 3, 6, 8, 24, 27, 108, 112, 560, 565, 3390, 3396, 23772, 23779, 190232, 190240, 1712160, 1712169, 17121690, 17121700, 188338700, 188338711, 2260064532, 2260064544, 29380839072, 29380839085, 411331747190, 411331747204, 6169976208060, 6169976208075, 98719619329200

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Robert Israel, Table of n, a(n) for n = 0..898

Crossrefs

Cf. A082458 (same, but start with 0), A019465 (start with 2), A019466 (start with 3).

Cf. A019460 .. A019463 & A082448 (similar, but first add, then multiply).

Programs

Maple

A[0]:= 2:
for n from 0 to 14 do
  A[2*n+1]:= (n+1)*A[2*n];
  A[2*n+2]:= (n+1)+A[2*n+1];
od:
seq(A[i],i=0..30); # Robert Israel, Dec 22 2015

Mathematica

a = {2}; Do[If[EvenQ@ Length@ a, AppendTo[a, Floor[Length[a]/2] Last@ a],
AppendTo[a, Last@ a + Floor[Length[a] /2]]], {k, 27}]; Rest@ a (* Michael De Vlieger, Dec 22 2015 *)

PARI

A019465(n,a=2)={for(i=2,n+1,if(bittest(i,0),a+=i\2,a*=i\2));a} \\ M. F. Hasler, Feb 25 2018

Formula

From Robert Israel, Dec 22 2015: (Start)

a(2*k) = 2*k! + Sum_{j=0..k-1} k!/j! = 2*k! + k*e*Gamma(k,1).

a(2*k+1) = 2*(k+1)! + Sum_{j=0..k-1} (k+1)!/j! = 2*(k+1)! + k*(k+1)*e*Gamma(k,1).

a(n) ~ (e+2)*(ceiling(n/2))!. (End)

Extensions

Edited by M. F. Hasler, Feb 25 2018