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a(n) = (4*n)!/(3*n+1)!.
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%I #25 Aug 31 2024 08:31:59

%S 1,1,8,132,3360,116280,5100480,271252800,16963914240,1220096908800,

%T 99225500774400,9003984596006400,901928094049382400,

%U 98856066097780992000,11768525894839633920000,1512185803617951221760000,208598907329474462760960000

%N a(n) = (4*n)!/(3*n+1)!.

%F E.g.f.: exp( 1/4 * Sum_{k>=1} binomial(4*k,k) * x^k/k ). - _Seiichi Manyama_, Feb 08 2024

%F a(n) = A000142(n)*A002293(n). - _Alois P. Heinz_, Feb 08 2024

%F From _Seiichi Manyama_, Aug 31 2024: (Start)

%F E.g.f. satisfies A(x) = 1/(1 - x*A(x)^3).

%F a(n) = Sum_{k=0..n} (3*n+1)^(k-1) * |Stirling1(n,k)|. (End)

%o (PARI) a(n) = (4*n)!/(3*n+1)!;

%o (Python)

%o from sympy import ff

%o def A365340(n): return ff(n<<2,n-1) # _Chai Wah Wu_, Sep 01 2023

%Y Cf. A001761, A001763, A052795, A365341.

%Y Cf. A004331, A061924.

%Y Cf. A370056, A370057, A370058.

%Y Cf. A000142, A002293.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Sep 01 2023