A162582 - OEIS

%I #7 Jul 04 2018 20:15:47

%S 1,2,6,10,146,282,826,1370,4204986,8408602,25223066,42037530,

%T 615687706,1189337882,3483938586,5778539290,2305851850537847066,

%U 4611703695297154842,13835111074334385946,23058518453371617050

%N G.f.: A(x) = exp( 2*Sum_{n>=1} A006519(n)^n * x^n/n ), where A006519(n) = highest power of 2 dividing n.

%H G. C. Greubel, <a href="/A162582/b162582.txt">Table of n, a(n) for n = 0..450</a>

%e G.f.: A(x) = 1 + 2*x + 6*x^2 + 10*x^3 + 146*x^4 + 282*x^5 + 826*x^6 + ...

%e log(A(x))/2 = 2^0*x + 2^2*x^2 + 2^0*x^3/3 + 2^8*x^4/4 + 2^0*x^5/5 + 2^6*x^6/6 + 2^0*x^7/7 + 2^24*x^8/8 + ... + A006519(n)^n*x^n/n + ...

%t nmax = 200; a[n_]:= SeriesCoefficient[Series[Exp[ Sum[2^(k*IntegerExponent[k, 2] + 1)*q^k/k, {k, 1, nmax}]], {q,0,nmax}], n]; Table[a[n], {n,0,50}] (* _G. C. Greubel_, Jul 04 2018 *)

%o (PARI) {a(n)=local(L=sum(m=1,n,2*(2^valuation(m,2))^m*x^m/m)+x*O(x^n));polcoeff(exp(L),n)}

%Y Cf. A162580, A162581, A155200, A006519, A000123.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jul 06 2009