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

0,5

Links

Table of n, a(n) for n=0..24.

Example

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!.

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

Prog

(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!))

Crossrefs

Cf. A087214, A128230, A128231.

Sequence in context: A026540 A351932 A329256 * A362352 A099099 A074082

Adjacent sequences: A128229 A128230 A128231 * A128233 A128234 A128235

Keyword

nonn

Author

Paul D. Hanna, Feb 20 2007

Status

approved