|
%I #15 Jul 12 2022 09:50:14
%S 2,8,2,24,2,8,2,64,2,8,2,24,2,8,2,160,2,8,2,24,2,8,2,64,2,8,2,24,2,8,
%T 2,384,2,8,2,24,2,8,2,64,2,8,2,24,2,8,2,160,2,8,2,24,2,8,2,64,2,8,2,
%U 24,2,8,2,896,2,8,2,24,2,8,2,64,2,8,2,24,2,8,2,160,2,8,2,24,2,8,2,64,2,8,2,24,2
%N a(n) = A001511(n)*2^A001511(n) where A001511(n) equals the 2-adic valuation of 2n.
%C 2n/2^A001511(n) is odd for n >= 1, so that A001511(n) is logarithmic in nature.
%H Antti Karttunen, <a href="/A183037/b183037.txt">Table of n, a(n) for n = 1..16383</a>
%F Logarithmic derivative of A183036.
%e L.g.f.: A(x) = 2*x + 8*x^2/2 + 2*x^3/3 + 24*x^4/4 + 2*x^5/5 + 8*x^6/6 + 2*x^7/7 + 64*x^8/8 + 2*x^9/9 + 8*x^10/10 + ...
%e The g.f. of A183036 begins:
%e exp(A(x)) = 1 + 2*x + 6*x^2 + 10*x^3 + 24*x^4 + 38*x^5 + 74*x^6 + ...
%t Array[# 2^# &[IntegerExponent[#, 2] + 1] &, 93] (* _Michael De Vlieger_, Nov 06 2018 *)
%o (PARI) {a(n)=valuation(2*n,2)*2^valuation(2*n,2)}
%o (Python)
%o def A183037(n): return (m:=n&-n)*m.bit_length()<<1 # _Chai Wah Wu_, Jul 12 2022
%Y Cf. A183036.
%K nonn
%O 1,1
%A _Paul D. Hanna_, Dec 19 2010
|
