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A193532 G.f.: x = Sum_{n>=1} x^n * ((1+x)^(n+1) - x^(n+1)) / (1+x)^a(n). 0

%I

%S 3,4,8,9,11,12,17,18,20,21,24,25,27,28,34,35,37,38,41,42,44,45,49,50,

%T 52,53,56,57,59,60,67,68,70,71,74,75,77,78,82,83,85,86,89,90,92,93,98,

%U 99,101,102,105,106,108,109,113,114,116,117,120,121,123,124,132,133,135,136,139,140,142,143,147,148,150,151,154,155,157,158,163,164,166,167,170

%N G.f.: x = Sum_{n>=1} x^n * ((1+x)^(n+1) - x^(n+1)) / (1+x)^a(n).

%F a(n) = n + floor(log_2(n+1)) + A011371(n+1) for n>=1, where A011371(n) = highest power of 2 dividing n!.

%e G.f.: x = x*((1+x)^2 - x^2)/(1+x)^3 + x^2*((1+x)^3 - x^3)/(1+x)^4 + x^3*((1+x)^4 - x^4)/(1+x)^8 + x^4*((1+x)^5 - x^5)/(1+x)^9 + x^5*((1+x)^6 - x^6)/(1+x)^11 + x^6*((1+x)^7 - x^7)/(1+x)^12 + x^7*((1+x)^8 - x^8)/(1+x)^17 + x^8*((1+x)^9 - x^9)/(1+x)^18 +...+ x^n*((1+x)^(n+1) - x^(n+1))/(1+x)^a(n) +...

%o (PARI) {a(n)=if(n<1,0,n+ floor(log(n+1+1/100)/log(2)) + valuation((n+1)!,2))}

%o (PARI) {a(n)=if(n<1,0,if(n==1,3,polcoeff(sum(m=1,n+1,x^m*((1+x)^(m+1)-x^(m+1))/(1+x +x^2*O(x^n))^if(m>=n,1,a(m)))+x^(n+1),n+1)))}

%Y Cf. A193259, A193260.

%K nonn

%O 1,1

%A _Paul D. Hanna_, Jul 29 2011

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Last modified June 12 19:57 EDT 2021. Contains 344962 sequences. (Running on oeis4.)