A112241 Expansion of exp(x/(1-2x-2x^2)).

1, 1, 5, 49, 601, 9281, 170941, 3662065, 89368049, 2446433281, 74212220341, 2470200090161, 89490288001225, 3504680581915969, 147513939627740141, 6639918363792119281, 318237954786998696161, 16178761263710217424385

Offset

0,3

Comments

In general, e.g.f. exp(x/(1-ax-bx^2)) has general term n!*sum{i=0..n, sum{j=0..n, a^j*(b/a)^(n-i-j)*C(i+j-1,j)C(j,n-i-j)/i!}}.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..300

Formula

E.g.f.: exp(x/(1-2*x-2*x^2)).

a(n) = n!*sum{i=0..n, sum{j=0..n, 2^j*C(i+j-1,j)*C(j,n-i-j)/i! } }.

Recurrence: a(n) = (4*n-3)*a(n-1) - 2*(n-2)*(n-1)*(4*n-13)*a(n-3) - 4*(n-4)*(n-3)*(n-2)*(n-1)*a(n-4). - Vaclav Kotesovec, Aug 15 2013

a(n) ~ 2^(-3/4)*3^(-1/8) * (1+sqrt(3))^n * exp(3^(-1/4)*sqrt(2*n)-n-1/12) * n^(n-1/4) * (1-7/(6*3^(3/4)*sqrt(2*n))). - Vaclav Kotesovec, Aug 15 2013

Mathematica

With[{nn=20}, CoefficientList[Series[Exp[x/(1-2x-2x^2)], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, May 12 2012 *)

Crossrefs

Sequence in context: A370097 A274671 A371364 * A216483 A243945 A297513

Adjacent sequences: A112238 A112239 A112240 * A112242 A112243 A112244

Keyword

easy,nonn

Author

Paul Barry, Aug 29 2005

Status

approved