1,2

Schenker sums without n-th term.

a(n)/n^n = Q(n) (called Ramanujan's function by Knuth)

Urn, n balls, with replacement: how many selections before a ball is chosen that was chosen already? Expected value is a(n)/n^n.

D. E. Knuth, The Art of Computer Programming, 3rd ed. 1997, Vol. 1, Addison-Wesley, Reading, MA, 1.2.11.3 p. 116

Marijke van Gans, Schenker sums

a(n) = Sum[k=0..n-1] n^k n!/k!

a(n)/n! = Sum[k=0..n-1] n^k/k! (first n terms of e^n power series)

E.g.f.: T/(1-T)^2, where T=T(x) is Euler's tree function (see A000169) - Len Smiley (smiley(AT)math.uaa.alaska.edu), Nov 28 2001

e.g. a(4) = (1*2*3*4) + 4*(2*3*4) + 4*4*(3*4) + 4*4*4*(4)

(UBASIC) 10 for N=1 to 42 : T=N^N : S=0

(UBASIC) 20 for K=N to 1 step -1 : T/=N : T*=K : S+=T : next K

(UBASIC) 30 print N, S : next N

(PARI) a(n)=sum(k=1, n, binomial(n, k)*n^(n-k)*k!) /* Michael Somos Jun 09 2004 */

a(n) = A063170(n) - n^n. Cf. A001865.

Sequence in context: A057817 A000405 A113352 this_sequence A134525 A125865 A134276

Adjacent sequences: A063166 A063167 A063168 this_sequence A063170 A063171 A063172

nonn,easy,nice

Marijke van Gans (marijke(AT)maxwellian.demon.co.uk)