A128231 Expansion of exp(x)/(1 - x^3/3!), where a(n) = 1 + binomial(n,3)*a(n-3).

1, 1, 1, 2, 5, 11, 41, 176, 617, 3445, 21121, 101806, 757901, 6040607, 37057385, 344844956, 3382739921, 25199021801, 281393484097, 3277874983450, 28726884853141, 374253333849011, 5047927474513001, 50875313074912712

Offset: 0

Author

Paul D. Hanna, Feb 20 2007

Keywords

• nonn

Examples

			E.g.f.: exp(x)/(1 - x^3/3!) = 1 + x + 1*x^2/2! + 2*x^3/3! + 5*x^4/4! + 11*x^5/5! + 41*x^6/6! + ... + a(n)*x^n/n! + ...
where a(n) = 1 + n*(n-1)*(n-2)*a(n-3)/3!.
		

Crossrefs

Cf. A087214, A128230, A128232.

Programs

Maple

restart: G(x):=2*exp(-x)/(x^3/3!+1): f[0]:=G(x): for n from 1 to 26 do f[n]:=diff(-f[n-1],x) od: x:=0: seq(f[n]/2,n=0..23); # Zerinvary Lajos, Apr 03 2009

PARI

a(n)=n!*polcoeff(exp(x+x*O(x^n))/(1-x^3/3! +x*O(x^n)),n)