A038159 a(n) = n*a(n-1) + 1, a(0) = 2.

2, 3, 7, 22, 89, 446, 2677, 18740, 149921, 1349290, 13492901, 148421912, 1781062945, 23153818286, 324153456005, 4862301840076, 77796829441217, 1322546100500690, 23805829809012421, 452310766371236000, 9046215327424720001, 189970521875919120022

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(n) = A033540(n+1) + 1.

a(n) = n! * (1 + Sum(1/k!, k=0..n)) = A000522(n) + n!. - Michael Somos, Mar 26 1999

E.g.f.: (1+exp(x))/(1-x).

a(n) = floor(n!*(e+1)), n>0. - Gary Detlefs, Jul 18 2010

D-finite with recurrence: a(n) +(-n-1)*a(n-1) +(n-1)*a(n-2)=0. - R. J. Mathar, Feb 16 2014

0 = +a(n)*(+a(n+1) -3*a(n+2) +a(n+3)) +a(n+1)*(+a(n+1) -a(n+3)) +a(n+2)*(+a(n+2)) if n>=0. - Michael Somos, Oct 23 2017

Example

G.f. = 2 + 3*x + 7*x^2+ 22*x^3 + 89*x^4 + 446*x^5 + 2677*x^6 + 18740*x^7 + ...

Mathematica

a[ n_] := If[ n < 0, 0, n! SeriesCoefficient[ (1 + Exp[x]) / (1 - x), {x, 0, n}]] (* Michael Somos, Sep 04 2013 *)
Range[0, 20]! CoefficientList[Series[(1 + Exp[x])/(1 - x), {x, 0, 20}], x] (* Vincenzo Librandi, Feb 17 2014 *)

Prog

(PARI) {a(n) = if( n<0, 0, n! * sum(k=0, n, 1/k!, 1))}; /* Michael Somos, Sep 04 2013 */

Crossrefs

Cf. A000522, A033540.

Sequence in context: A010738 A114599 A094062 * A077210 A324620 A151908

Adjacent sequences: A038156 A038157 A038158 * A038160 A038161 A038162

Keyword

nonn

Author

N. J. A. Sloane

Status

approved