A228938 E.g.f.: (2 + exp(3*x)) / (4 - exp(3*x)).

1, 2, 10, 66, 570, 6162, 80010, 1212066, 20983770, 408687282, 8844164010, 210530630466, 5467167038970, 153805368043602, 4659779072312010, 151259403573751266, 5237308594356166170, 192673897986624475122, 7505181282611209004010, 308589102795660836942466

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

E.g.f. A(x) satisfies:

(1) A'(x) = -1 + A(x) + 2*A(x)^2.

(2) A(x) = exp(x + Integral 2*A(x) - 1/A(x) dx).

(3) A(x) = 1 + Series_Reversion( Integral 1/((2+x)*(1+2*x)) dx ).

a(n) ~ n!/2 * (3/(2*log(2)))^(n+1). - Vaclav Kotesovec, Dec 19 2013

Example

E.g.f.: A(x) = 1 + 2*x + 10*x^2/2! + 66*x^3/3! + 570*x^4/4! + 6162*x^5/5! +...

Mathematica

CoefficientList[Series[(2+E^(3*x))/(4-E^(3*x)), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Dec 19 2013 *)

Prog

(PARI) {a(n)=local(A=1+x, X=x+x*O(x^n)); n!*polcoeff((2+exp(3*X))/(4-exp(3*X)), n)}
for(n=0, 20, print1(a(n), ", "))
(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=exp(x+intformal(2*A-1/A+x*O(x^n)))); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A190818.

Sequence in context: A361448 A346417 A108205 * A245000 A108397 A325995

Adjacent sequences: A228935 A228936 A228937 * A228939 A228940 A228941

Keyword

nonn

Author

Paul D. Hanna, Dec 18 2013

Status

approved