A019463 Add 1, multiply by 1, add 2, multiply by 2, etc., start with 1.

1, 2, 2, 4, 8, 11, 33, 37, 148, 153, 765, 771, 4626, 4633, 32431, 32439, 259512, 259521, 2335689, 2335699, 23356990, 23357001, 256927011, 256927023, 3083124276, 3083124289, 40080615757, 40080615771, 561128620794, 561128620809, 8416929312135, 8416929312151, 134670868994416

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..900
• Nick Hobson, Python program for this sequence.

Crossrefs

Cf. A019461 (same, but start with 0), A019460 (start with 2), A019462, (start with 3), A082448. (start with 4).

Cf. A082458, A019464, A019465, A019466 (similar, but first multiply, then add).

Cf. A019762.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, (t->
      `if`(n::odd, t+(n+1)/2, t*n/2))(a(n-1)))
    end:
seq(a(n), n=0..32);  # Alois P. Heinz, Jan 16 2024

Mathematica

For[i=1;lst={1},i<15,i++,AppendTo[lst,i+Last[lst]];AppendTo[lst,i Last[lst]]];lst (* Harvey P. Dale, Feb 25 2012 *)
FoldList[If[OddQ[#2], #1 + (#2 + 1)/2, #1 * (#2/2)]&, 1, Range[32]] (* AnneMarie Torresen, Nov 26 2023 *)

PARI

A019463(n, a=1)={for(i=2, n+1, if(bittest(i, 0), a*=i\2, a+=i\2)); a} \\ M. F. Hasler, Feb 25 2018

Formula

Limit_{n->oo} a(2n)/n! = 1 + 2e = 1 + A019762. - Jon E. Schoenfield, Jan 16 2024

Extensions

Edited by M. F. Hasler, Feb 25 2018