A128232 Expansion of exp(x)/(1 - x^4/4!), where a(n) = 1 + C(n,4)*a(n-4).

1, 1, 1, 1, 2, 6, 16, 36, 141, 757, 3361, 11881, 69796, 541256, 3364362, 16217566, 127028721, 1288189281, 10294947721, 62859285817, 615454153246, 7709812846786, 75307542579116, 556618975909536, 6539815832391997

Offset: 0

Author

Paul D. Hanna, Feb 20 2007

Keywords

• nonn

Examples

			E.g.f.: exp(x)/(1 - x^4/4!) = 1 + x + 1*x^2/2! + 1*x^3/3! + 2*x^4/4! + 6*x^5/5! + 16*x^6/6! +... + a(n)*x^n/n! +...
where a(n) = 1 + n*(n-1)*(n-2)*(n-3)*a(n-4)/4!.
		

Crossrefs

Cf. A087214, A128230, A128231.

Programs

Maple

G(x):=exp(x)/(1-x^4/4!): f[0]:=G(x): for n from 1 to 26 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=0..24); # Zerinvary Lajos, Apr 03 2009

PARI

a(n)=n!*polcoeff(exp(x+x*O(x^n))/(1-x^4/4! +x*O(x^n)),n)

PARI

/* Recurrence: */ a(n)=if(n<0,0,if(n<4,1,1 + n*(n-1)*(n-2)*(n-3)*a(n-4)/4!))