A395174 a(n) = (2*n)! * [x^(2*n)] C(x)^3, where C(x) satisfies C(x) = cosh( Integral C(x)^5 dx ).

1, 3, 81, 6003, 866241, 205785603, 72824987601, 35922903140403, 23555673807464961, 19815995152757904003, 20803094759381633159121, 26658027314982853570374003, 40950365987475777494675890881, 74279308405714371324239340912003, 157078062821547751478860528496041041

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,3).

Prog

(PARI) a(n, k=3) = if(n==0, 1, k*(k+5)*a(n-1, k+10)-k*(k+4)*a(n-1, k+8));

Crossrefs

Column k=3 of A395172.

Cf. A079484, A281184, A326328, A395147.

Sequence in context: A355157 A207229 A223717 * A223825 A207222 A207007

Adjacent sequences: A395171 A395172 A395173 * A395175 A395176 A395177

Keyword

nonn

Author

Seiichi Manyama, Apr 15 2026

Status

approved