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%I #13 Jul 30 2021 10:20:18
%S 1,0,6,45,461,5020,57812,691586,8512048,107095262,1371219004,
%T 17808830924,234048288772,3106795261083,41593689788637,
%U 560980967638479,7614970691479315,103957059568762775,1426355910771621805,19658792867492660060,272046427837226505466
%N a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(6*k,k) / (5*k + 1).
%H Seiichi Manyama, <a href="/A346682/b346682.txt">Table of n, a(n) for n = 0..856</a>
%F G.f. A(x) satisfies: A(x) = 1 / (1 + x) + x * (1 + x)^5 * A(x)^6.
%F a(n) ~ 2^(6*n + 6) * 3^(6*n + 13/2) / (49781 * sqrt(Pi) * n^(3/2) * 5^(5*n + 3/2)). - _Vaclav Kotesovec_, Jul 30 2021
%t Table[Sum[(-1)^(n - k) Binomial[6 k, k]/(5 k + 1), {k, 0, n}], {n, 0, 20}]
%t nmax = 20; A[_] = 0; Do[A[x_] = 1/(1 + x) + x (1 + x)^5 A[x]^6 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%o (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(6*k, k)/(5*k + 1)); \\ _Michel Marcus_, Jul 29 2021
%Y Cf. A002295, A032357, A188678, A346065, A346666.
%Y Cf. A346680, A346681, A346683, A346684.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jul 29 2021
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