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

0,1

Links

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

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)

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 *)

Prog

(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

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).

Sequence in context: A100948 A035571 A079069 * A077074 A163493 A321405

Adjacent sequences: A019462 A019463 A019464 * A019466 A019467 A019468

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Edited by M. F. Hasler, Feb 25 2018

Status

approved