OFFSET
0,2
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
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..403
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
EXAMPLE
G.f. = 1 + 3*x + 11*x^2 + 59*x^3 + 443*x^4 + 4283*x^5 + 50363*x^6 + 695483*x^7 + ...
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 *)
PROG
(PARI) {a(n) = sum(k=0, n, 2^k * k!)}; /* Michael Somos, Sep 27 2017 */
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 02 2005
STATUS
approved