A085644 a(0) = 1; a(n+1) = a(n)*2n + 2n + 1.

1, 1, 5, 25, 157, 1265, 12661, 151945, 2127245, 34035937, 612646885, 12252937721, 269564629885, 6469551117265, 168208329048917, 4709833213369705, 141294996401091181, 4521439884834917825, 153728956084387206085, 5534242419037939419097, 210301211923441697925725

Offset: 0

Author

Cino Hilliard, Aug 19 2003

Keywords

• nonn
• easy

Comments

Sum of reciprocals = 2.2472460058071954531775930749...

Crossrefs

a(n) = 2 * A010844(n-1) - 1 = A007566(n-1) - 2n - 2 for n>=1.

Programs

Maple

a:= proc(n) option remember;
     `if`(n=0, 1, 2*((n-1)*a(n-1)+n)-1)
    end:
seq(a(n), n=0..20);  # Alois P. Heinz, Mar 14 2023

Mathematica

nxt[{n_,a_}]:={n+1,a*2n+2n+1}; Transpose[NestList[nxt,{1,1},20]][[2]] (* Harvey P. Dale, Aug 06 2016 *)

PARI

sum2x(n) = { s=1; sr=0; forstep(x=2,n,2, s=x*(s+1)+1; print1(s","); sr += 1.0/s; ); print(); print(sr) }

Extensions

a(0)=1 prepended and edited by Alois P. Heinz, Mar 14 2023