OFFSET
1,2
COMMENTS
LINKS
T. Matsui and K. Ano, Lower Bounds for Bruss' Odds Problem with Multiple Stoppings, arXiv:1204.5537 [math.NT], 2012-2017.
EXAMPLE
1, 3/2, 47/24, 2761/1152, 4162637/1474560, 380537052235603/117413668454400, 705040594914523588948186792543/193003573558876719588311040000
MATHEMATICA
la[1]=1; alfa[k_, 1]=1/k!; alfa[k_, k_]:=1; la[k_]:=la[k]=1-alfa[k, k-1];
alfa[k_, kp_]:=alfa[k, kp]= la[kp]^(1+k-kp)/(1+k-kp)!+Sum[la[kp]^b/b! alfa[k-b, kp-1], {b, 0, k-kp}];
S[n_]:=Sum[la[i], {i, 1, n}];
Table[Numerator@S[n], {n, 1, 10}]
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
José María Grau Ribas, May 28 2022
STATUS
approved