A395175 a(n) = (2*n)! * [x^(2*n)] C(x)^4, where C(x) satisfies C(x) = cosh( Integral C(x)^5 dx ).

1, 4, 120, 9504, 1440000, 355567104, 129927214080, 65869132898304, 44237770918133760, 38013522097823023104, 40676946478220020285440, 53038454493359082521493504, 82781759608022968011608555520, 152379937009884305958263014293504, 326666022628016700248241314621030400

Offset

0,2

Links

Table of n, a(n) for n=0..14.

Formula

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).

Prog

(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));

Crossrefs

Column k=4 of A395172.

Sequence in context: A203033 A395488 A307935 * A001332 A071304 A213957

Adjacent sequences: A395172 A395173 A395174 * A395176 A395177 A395178

Keyword

nonn

Author

Seiichi Manyama, Apr 15 2026

Status

approved