cp's OEIS Frontend

A376282 G.f. A(x) satisfies A(x) = (1 + 9*x*A(x)^7)^(1/3).

%I A376282 #33 Aug 04 2025 14:21:05
%S A376282 1,3,54,1368,40365,1299078,44223732,1565864784,57079952046,
%T A376282 2127818007315,80742077597610,3108398557803480,121107814518484872,
%U A376282 4766365291226837508,189209375036491438800,7567095678024459993120,304603864960375133224533,12331716699093681951702810
%N A376282 G.f. A(x) satisfies A(x) = (1 + 9*x*A(x)^7)^(1/3).
%H A376282 Paolo Xausa, <a href="/A376282/b376282.txt">Table of n, a(n) for n = 0..600</a>
%F A376282 a(n) = 9^n * binomial(7*n/3 + 1/3,n)/(7*n+1).
%F A376282 G.f. A(x) satisfies A(x) = 1/A(-x*A(x)^11). - _Seiichi Manyama_, Jun 20 2025
%F A376282 D-finite with recurrence 8*n*(n-1)*(n-2)*(4*n-5)*(2*n-1)*(4*n+1)*a(n) -189*(7*n-11)*(7*n-17)*(7*n-2)*(7*n-20)*(7*n-5)*(7*n-8)*a(n-3)=0. - _R. J. Mathar_, Jul 30 2025
%t A376282 A376282[n_] := 9^n*Binomial[(7*n + 1)/3, n]/(7*n + 1);
%t A376282 Array[A376282, 20, 0] (* _Paolo Xausa_, Aug 04 2025 *)
%o A376282 (PARI) a(n) = 9^n*binomial(7*n/3+1/3, n)/(7*n+1);
%Y A376282 Cf. A004987, A008931, A078532, A245114, A376636.
%K A376282 nonn
%O A376282 0,2
%A A376282 _Seiichi Manyama_, Oct 23 2024