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a(n)=(-36^n/18)*B(2n,1/6)/B(2n,1/3) where B(n,x) is the n-th Bernoulli polynomial.
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%I #12 Nov 15 2019 08:58:45

%S 1,63,2511,92583,3352671,120873303,4353033231,156723545223,

%T 5642176768191,203119525916343,7312313393341551,263243376303474663,

%U 9476762394213697311,341163453817290588183,12281884406052838539471

%N a(n)=(-36^n/18)*B(2n,1/6)/B(2n,1/3) where B(n,x) is the n-th Bernoulli polynomial.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (45,-324).

%F a(n)=9^n/18*(4^n-2)

%F a(n)=9^(n-1)/2*(2^(2n)-2) - _Harvey P. Dale_, Mar 09 2018

%F G.f.: x*(1+18*x) / ( (36*x-1)*(9*x-1) ). - _R. J. Mathar_, Nov 15 2019

%t LinearRecurrence[{45,-324},{1,63},20] (* _Harvey P. Dale_, Mar 09 2018 *)

%o (PARI) B(n,x)=sum(i=0,n,binomial(n,i)*bernfrac(i)*x^(n-i));a(n)=(-36^n/18)*B(n,1/6)/B(n,1/3)

%Y Cf. A096054.

%K nonn,easy

%O 1,2

%A _Benoit Cloitre_, Jun 19 2004

%E Incorrect recurrence formula deleted by _Harvey P. Dale_, Mar 09 2018