Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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