cp's OEIS Frontend

A193365 a(n) = A220371(n)/(4*A220371(n-1)).

%I A193365 #14 Jun 02 2025 04:14:48
%S A193365 15,126,143,1020,399,1150,783,8184,1295,3198,1935,9212,2703,6270,3599,
%T A193365 65520,4623,10366,5775,25596,7055,15486,8463,73720,9999,21630,11663,
%U A193365 50172,13455,28798,15375,524256,17423,36990
%N A193365 a(n) = A220371(n)/(4*A220371(n-1)).
%C A193365 This sequence is, via A220371, related to A220002, which is related to the Catalan numbers.
%C A193365 Information about the peculiar structure of the a(n) can be found in A220466.
%F A193365 a(n) = A220371(n)/(4*A220371(n-1))
%F A193365 a(2^p*(2*n-1)) = 2^p*(2^(2*p+4)*(2*n-1)^2-1), p >= 0.
%p A193365 nmax:= 34: for p from 0 to ceil(simplify(log[2](nmax))) do for n from 1 to ceil(nmax/(p+2)) do a(2^p*(2*n-1)) := 2^p*(2^(2*p+4)*(2*n-1)^2-1) od: od: seq(a(n), n=1..nmax);
%t A193365 b[n_] := b[n] = 2^(2n) Product[2i+1, {i, 1, 2n}] GCD[n!, 2^n];
%t A193365 a[n_] := b[n]/(4 b[n-1]);
%t A193365 Array[a, 34] (* _Jean-François Alcover_, Jun 26 2019 *)
%o A193365 (Sage)
%o A193365 def A193365_list(len):
%o A193365     a = {}; z = 1; s = 0; p = 1
%o A193365     while s < len:
%o A193365         i = s; z += z
%o A193365         while i < len:
%o A193365             a[i] = p*((4*i+4)^2-1)
%o A193365             i += z
%o A193365         s += s + 1; p += p
%o A193365     return [a[i] for i in range(len)]
%o A193365 A193365_list(30)  # _Peter Luschny_, Dec 22 2012
%Y A193365 Cf. A220466
%K A193365 nonn,easy
%O A193365 1,1
%A A193365 _Johannes W. Meijer_, Dec 21 2012