A127944 - OEIS

%I #12 Nov 15 2022 18:01:43

%S 0,0,0,2,3,7,11,17,21,29,37,47,56,68,80,94,105,121,137,155,172,192,

%T 212,234,254,278,302,328,353,381,409,439,465,497,529,563,596,632,668,

%U 706,742,782,822,864,905,949,993,1039,1082,1130,1178,1228,1277

%N Partial sums of A093049.

%H G. C. Greubel, <a href="/A127944/b127944.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = log_2(2^C(n+1,2)/denominator(C(2n,n)/4^n)).

%F a(n) = A000217(n) - A005187(n).

%F a(n) = log_2(A127943(n)).

%t Table[Log2[2^Binomial[n + 1, 2]/Denominator[Binomial[2 n, n]/4^n]], {n, 0, 100}] (* _G. C. Greubel_, May 01 2018 *)

%t Accumulate[Join[{0},Table[n-1-IntegerExponent[n,2],{n,80}]]] (* _Harvey P. Dale_, Nov 15 2022 *)

%o (Magma) [Floor(Log(2,(2^Binomial(n+1,2) / Denominator(Binomial(2*n,n) / 4^n)))): n in [0..80]]; // _Vincenzo Librandi_, May 02 2018

%K easy,nonn

%O 0,4

%A _Paul Barry_, Feb 08 2007