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A214691 G.f.: A(x) = Sum_{n>=0} x^n * Product_{k=1..n} (2^(2*k-1) - 1) / (1 + 2^(2*k-1)*x). 1

%I #4 Jul 26 2012 00:23:01

%S 1,1,5,151,19025,9702751,19851828545,162586475783551,

%T 5327308465523832065,698250320576208668759551,

%U 366082867573618138109269955585,767730685732013278335855487355082751,6440190236715680978727827356359771295535105

%N G.f.: A(x) = Sum_{n>=0} x^n * Product_{k=1..n} (2^(2*k-1) - 1) / (1 + 2^(2*k-1)*x).

%C A variant of A005014. Equals row sums (unsigned) of triangle A214690.

%F a(n) = 2*(4^(n-1) - 1)*a(n-1) - (-1)^n for n>0 with a(0)=1.

%o (PARI) {a(n)=if(n==0,1,2*(4^(n-1)-1)*a(n-1) - (-1)^n)}

%o (PARI) {a(n)=local(A=x); A=sum(m=0, n, x^m*prod(j=1, m, (2^(2*j-1)-1)/(1+x*2^(2*j-1))+x*O(x^n))); polcoeff(A, n, x)}

%o for(n=0, 20, print1(a(n), ", "));

%Y Cf. A005014 (variant), A214690.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jul 26 2012

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)