A394478 a(n) = (2*n)! * [x^(2*n)] cosh(x)^2 / cos(x).

1, 3, 25, 363, 8625, 317523, 17012425, 1255133883, 122088067425, 15141060001443, 2331848239989625, 436618890764872203, 97679144582957195025, 25732113033687351698163, 7884197446631511741699625, 2779950036439570315860031323, 1117657942134184862482265119425

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = (0^n + 4^n)/2 - Sum_{k=0..n-1} (-1)^(n-k) * binomial(2*n,2*k) * a(k).

a(n) = (1/2) * Sum_{k=0..n} (0^(n-k) + 4^(n-k)) * binomial(2*n,2*k) * A000364(k).

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=(0^i+4^i)/2-sum(j=0, i-1, (-1)^(i-j)*binomial(2*i, 2*j)*v[j+1])); v;

Crossrefs

Cf. A000795, A395296, A395297, A395298.

Cf. A000364

Sequence in context: A129506 A143139 A231637 * A377829 A295765 A380674

Adjacent sequences: A394473 A394474 A394475 * A394479 A394480 A394481

Keyword

nonn

Author

Seiichi Manyama, Apr 18 2026

Status

approved