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A371927 Expansion of 1/(1 - x/(1 - 8*x^2)^(1/4)).

%I A371927 #26 Dec 20 2024 17:23:50
%S A371927 1,1,1,3,5,17,33,113,237,803,1769,5915,13493,44547,104337,340527,
%T A371927 814397,2630857,6399865,20486905,50548997,160507953,400834465,
%U A371927 1263577141,3188428301,9985916077,25426685961,79168607025,203193847381,629311885861,1626634117809
%N A371927 Expansion of 1/(1 - x/(1 - 8*x^2)^(1/4)).
%F A371927 a(n) = Sum_{k=0..floor(n/2)} 8^k * binomial((n+2*k)/4-1,k).
%p A371927 A371927 := proc(n)
%p A371927     add(8^k*binomial((n+2*k)/4-1,k),k=0..floor(n/2)) ;
%p A371927 end proc:
%p A371927 seq(A371927(n),n=0..70) ; # _R. J. Mathar_, Jun 07 2024
%t A371927 CoefficientList[Series[1/(1-x/(1-8x^2)^(1/4)),{x,0,30}],x] (* _Harvey P. Dale_, Dec 20 2024 *)
%o A371927 (PARI) a(n) = sum(k=0, n\2, 8^k*binomial((n+2*k)/4-1, k));
%Y A371927 Cf. A373509, A004981.
%K A371927 nonn
%O A371927 0,4
%A A371927 _Seiichi Manyama_, Jun 07 2024