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A075055 Smallest integer of the form product (n+1)(n+2)...(n+k)/n!.

%I A075055 #20 Feb 05 2025 21:42:52
%S A075055 1,1,6,20,70,252,7,3432,12870,48620,184756,705432,2704156,10400600,
%T A075055 40116600,178296,601080390,2333606220,9075135300,35345263800,
%U A075055 137846528820,538257874440,2104098963720,8233430727600,32247603683100,126410606437752,495918532948104
%N A075055 Smallest integer of the form product (n+1)(n+2)...(n+k)/n!.
%C A075055 Differs from A000984 at positions in A058008.
%H A075055 Alois P. Heinz, <a href="/A075055/b075055.txt">Table of n, a(n) for n = 0..1664</a>
%e A075055 a(6) = 7 = 7*8*9*10/6! = 5040/720.
%p A075055 a:= proc(n) option remember; local k, t; t:= 1/n!;
%p A075055       for k while denom(t)>1 do t:= t*(n+k) od; t
%p A075055     end:
%p A075055 seq(a(n), n=0..28);  # _Alois P. Heinz_, Feb 05 2025
%t A075055 a[n_] := Catch[ For[ k = n-2, True, k++, If[ IntegerQ[an = (n+k)!/n!^2], Throw[an]]]]; a[1]=1; Table[a[n], {n, 1, 24}] (* _Jean-François Alcover_, Jun 28 2012 *)
%Y A075055 Cf. A075054.
%K A075055 nice,nonn
%O A075055 0,3
%A A075055 _Amarnath Murthy_, Sep 07 2002
%E A075055 More terms from _Sascha Kurz_, Feb 02 2003
%E A075055 a(0)=1 prepended by _Alois P. Heinz_, Feb 05 2025