A395175 - OEIS

%I #8 Apr 15 2026 09:29:40

%S 1,4,120,9504,1440000,355567104,129927214080,65869132898304,

%T 44237770918133760,38013522097823023104,40676946478220020285440,

%U 53038454493359082521493504,82781759608022968011608555520,152379937009884305958263014293504,326666022628016700248241314621030400

%N a(n) = (2*n)! * [x^(2*n)] C(x)^4, where C(x) satisfies C(x) = cosh( Integral C(x)^5 dx ).

%F Let A(n,k) = (2*n)! * [x^(2*n)] C(x)^k. A(0,k) = 1 and A(n,k) = k*(k+5) * A(n-1,k+10) - k*(k+4) * A(n-1,k+8) for n > 0. a(n) = A(n,4).

%o (PARI) a(n, k=4) = if(n==0, 1, k*(k+5)*a(n-1, k+10)-k*(k+4)*a(n-1, k+8));

%Y Column k=4 of A395172.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 15 2026