A128230 Expansion of exp(x)/(1 - x - x^2/2!), where a(n) = 1 + n*a(n-1) + C(n,2)*a(n-2).

1, 2, 6, 25, 137, 936, 7672, 73361, 801705, 9856342, 134640146, 2023140417, 33163934641, 588936102860, 11263023492372, 230783643185881, 5044101110058737, 117136294344278346, 2880200768035996990

Offset: 0

Author

Paul D. Hanna, Feb 20 2007

Keywords

• nonn

Examples

			E.g.f.: exp(x)/(1 - x - x^2/2!) = 1 + 2*x + 6*x^2/2! + 25*x^3/3! + 137*x^4/4! + 936*x^5/5! + 7672*x^6/6! +... + a(n)*x^n/n! +...
where a(n) = 1 + n*a(n-1) + n*(n-1)*a(n-2)/2.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A087214, A000629, A128231, A128232.

Programs

Mathematica

CoefficientList[Series[E^x/(1-x-x^2/2), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 20 2012 *)

PARI

a(n)=n!*polcoeff(exp(x+x*O(x^n))/(1-x-x^2/2! +x*O(x^n)),n)

Formula

a(n) ~ n!*exp(sqrt(3)-1)*((1+sqrt(3))/2)^(n+1)/sqrt(3) . - Vaclav Kotesovec, Oct 20 2012