A381281 - OEIS

%I #8 Feb 19 2025 03:38:05

%S 1,1,2,33,240,2145,33120,480753,7878528,158696577,3384322560,

%T 78934776129,2053186983936,57231998680545,1714372871178240,

%U 55323775198258065,1899762412262031360,69264871449203672577,2677542944055160209408,109197154520146527569505

%N Expansion of e.g.f. 1/(1 - x * cosh(3*x)).

%C As stated in the comment of A185951, A185951(n,0) = 0^n.

%F a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} 9^k * (2*k+1) * binomial(n,2*k+1) * a(n-2*k-1).

%F a(n) = Sum_{k=0..n} k! * 3^(n-k) * A185951(n,k).

%o (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));

%o a(n) = sum(k=0, n, k!*3^(n-k)*a185951(n, k));

%Y Cf. A205571, A381280.

%Y Cf. A185951.

%K nonn,new

%O 0,3

%A _Seiichi Manyama_, Feb 18 2025