|
%I #3 Mar 10 2015 23:15:38
%S 1,5,705,904405,4852631105,74099113400805,2586129891894933505,
%T 178907219873738420449205,22190820320340007699602667905,
%U 4580340005051337829651272441809605,1485137988777113358037521465779043594305,722514649061693644099760448944719529057242005
%N O.g.f.: exp( Sum_{n>=1} A000364(2*n)*x^n/n ), where A000364 is the Euler numbers.
%C a(n) == 5 (mod 100) for n>=1 (conjecture).
%e O.g.f.: A(x) = 1 + 5*x + 705*x^2 + 904405*x^3 + 4852631105*x^4 +...
%e where
%e log(A(x)) = 5*x + 1385*x^2/2 + 2702765*x^3/3 + 19391512145*x^4/4 + 370371188237525*x^5/5 + 15514534163557086905*x^6/6 + +...+ A000364(2*n)*x^n/n +...
%o (PARI) /* By definition */
%o {A000364(n)=polcoeff(sum(m=0, n, (2*m)!/2^m * x^m/prod(k=1, m, 1+k^2*x+x*O(x^n))), n)}
%o {a(n)=local(A=1);A=exp(sum(m=1,n,A000364(2*m)*x^m/m) +x*O(x^n));polcoeff(A,n)}
%o for(n=0,20,print1(a(n),", "))
%Y Cf. A255881, A255895, A000364.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Mar 10 2015
| 