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Numerator of row 4 in A051714(n) or row 3 in A176672(n).
3

%I #11 Aug 03 2014 16:52:44

%S 0,1,1,2,5,5,7,28,3,15,55,22,13,91,35,40,34,51,57,190,35,77,253,92,25,

%T 325,117,126,203,145,155,496,44,187,595,210,111,703,247,260,205,287,

%U 301,946,165,345,1081,376,98,1225,425

%N Numerator of row 4 in A051714(n) or row 3 in A176672(n).

%C Akiyama-Tanigawa algorithm from 1/n leads to Bernoulli A164555(n)/A027642(n):

%C 1, 1/2, 1/3, 1/4,

%C 1/2, 1/3, 1/4, 1/5,

%C 1/6, 1/6, 3/20, 2/15, =A026741(n+1)/A045896(n+1),

%C 0, 1/30, 1/20, 2/35, 5/84, 5/84, 7/120, 28/495 =a(n)/b(n).

%t a[0, k_] := 1/(k+1); a[n_, k_] := a[n, k] = (k+1)*(a[n-1, k] - a[n-1, k+1]); Table[a[3, k], {k, 0, 50}] // Numerator (* _Jean-François Alcover_, Sep 19 2012 *)

%Y Cf. A193220 (denominators).

%K nonn,frac

%O 0,4

%A _Paul Curtz_, Aug 28 2011