A394478 - OEIS

%I #21 Apr 20 2026 09:22:15

%S 1,3,25,363,8625,317523,17012425,1255133883,122088067425,

%T 15141060001443,2331848239989625,436618890764872203,

%U 97679144582957195025,25732113033687351698163,7884197446631511741699625,2779950036439570315860031323,1117657942134184862482265119425

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

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

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

%o (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;

%Y Cf. A000795, A395296, A395297, A395298.

%Y Cf. A000364

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 18 2026