A255912 O.g.f.: exp( Sum_{n>=1} A000364(2*n)*x^n/n ), where A000364 is the Euler numbers.

1, 5, 705, 904405, 4852631105, 74099113400805, 2586129891894933505, 178907219873738420449205, 22190820320340007699602667905, 4580340005051337829651272441809605, 1485137988777113358037521465779043594305, 722514649061693644099760448944719529057242005

Offset: 0

Author

Paul D. Hanna, Mar 10 2015

Keywords

• nonn

Comments

a(n) == 5 (mod 100) for n>=1 (conjecture).

Examples

			O.g.f.: A(x) = 1 + 5*x + 705*x^2 + 904405*x^3 + 4852631105*x^4 +...
where
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 +...
		

Crossrefs

Cf. A255881, A255895, A000364.

Programs

PARI

/* By definition */
{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)}
{a(n)=local(A=1);A=exp(sum(m=1,n,A000364(2*m)*x^m/m) +x*O(x^n));polcoeff(A,n)}
for(n=0,20,print1(a(n),", "))