A112368 a(n) = Sum_{i=0..n} 2^i*i!.

1, 3, 11, 59, 443, 4283, 50363, 695483, 11017403, 196811963, 3912703163, 85662309563, 2047652863163, 53059407256763, 1481388530277563, 44331262220901563, 1415527220320869563, 48036189795719781563, 1726380042510080613563, 65503446445655792229563, 2616586102571484256869563

Offset: 0

Author

N. J. A. Sloane, Dec 02 2005

Keywords

• nonn

Comments

a(n) is divisible by 73 for all n >= 72, hence this sequence contains only a finite number of primes. - Giovanni Resta, Mar 11 2017

Partial sums of A000165. One less than A004400. one more than A112369. - Michael Somos, Sep 27 2017

Examples

			G.f. = 1 + 3*x + 11*x^2 + 59*x^3 + 443*x^4 + 4283*x^5 + 50363*x^6 + 695483*x^7 + ...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..403

Crossrefs

Cf. A000165, A004400, A112369.

Programs

Mathematica

s = 1; lst = {s}; Do[s += n!!; AppendTo[lst, s], {n, 2, 38, 2}]; lst (* Zerinvary Lajos, Jul 13 2009 *)
a[ n_] := Sum[ 2^k k!, {k, 0, n}]; (* Michael Somos, Sep 27 2017 *)

PARI

{a(n) = sum(k=0, n, 2^k * k!)}; /* Michael Somos, Sep 27 2017 */

Formula

0 = +a(n)*(+2*a(n+1) - 3*a(n+2) + a(n+3)) + a(n+1)*(-a(n+1) + a(n+2) - a(n+3)) + a(n+2)*(a(n+2)) for all n>=0. - Michael Somos, Sep 27 2017