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A386392 a(n) = 4 * binomial(7*n+4,n)/(7*n+4).

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%I A386392 #23 Jul 20 2025 15:02:05
%S A386392 1,4,34,368,4495,59052,814506,11633440,170574723,2552698720,
%T A386392 38832808586,598724403680,9335085772194,146936230074004,
%U A386392 2331703871687400,37263447339612480,599206511767593099,9688121925389895636,157401957319775436400,2568427016865897264000
%N A386392 a(n) = 4 * binomial(7*n+4,n)/(7*n+4).
%H A386392 Wikipedia, <a href="https://en.wikipedia.org/wiki/Fuss-Catalan_number">Fuss-Catalan number</a>
%F A386392 a(n) = r * binomial(n*p+r,n)/(n*p+r), the Fuss-Catalan number with p=7 and r=4.
%F A386392 a(n) = A386380(6*n+3).
%F A386392 G.f. A(x) satisfies A(x) = (1 + x*A(x)^(p/r))^r, where p=7, r=4.
%F A386392 G.f.: B(x)^4, where B(x) is the g.f. of A002296.
%o A386392 (PARI) apr(n, p, r) = r*binomial(n*p+r, n)/(n*p+r);
%o A386392 a(n) = apr(n, 7, 4);
%Y A386392 Cf. A118971, A212073, A234463, A234507, A234527, A234870.
%Y A386392 Cf. A002296, A386380.
%K A386392 nonn
%O A386392 0,2
%A A386392 _Seiichi Manyama_, Jul 20 2025