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a(n) = (5*n)!/(4*n+1)!.
7

%I #22 Aug 31 2024 08:31:00

%S 1,1,10,210,6840,303600,17100720,1168675200,93963542400,8691104822400,

%T 909171781056000,106137499051584000,13679492361575040000,

%U 1929327666754295808000,295570742023171270656000,48877281133334949335040000,8677556868736487617966080000

%N a(n) = (5*n)!/(4*n+1)!.

%F E.g.f.: exp( 1/5 * Sum_{k>=1} binomial(5*k,k) * x^k/k ). - _Seiichi Manyama_, Feb 08 2024

%F a(n) = A000142(n)*A002294(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)^4).

%F a(n) = Sum_{k=0..n} (4*n+1)^(k-1) * |Stirling1(n,k)|. (End)

%o (PARI) a(n) = (5*n)!/(4*n+1)!;

%o (Python)

%o from sympy import ff

%o def A365341(n): return ff(5*n,n-1) # _Chai Wah Wu_, Sep 01 2023

%Y Cf. A001761, A001763, A052795, A365340.

%Y Cf. A004343.

%Y Cf. A000142, A002294.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Sep 01 2023