A218438 G.f.: 1 / ( (1 + x^2 - x^3)^2 * (1 - x - 2*x^2 - x^3) ).

1, 1, 1, 6, 12, 19, 48, 110, 218, 470, 1040, 2208, 4710, 10184, 21879, 46879, 100767, 216570, 464952, 998613, 2145312, 4607724, 9896436, 21257196, 45658624, 98068864, 210642412, 452440320, 971794317, 2087314717, 4483345053, 9629771966, 20683772420, 44426659559

Offset: 0

Author

Paul D. Hanna, Oct 28 2012

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + x^2 + 6*x^3 + 12*x^4 + 19*x^5 + 48*x^6 + 110*x^7 +...
where
log(A(x)) = x + x^2/2 + 16*x^3/3 + 25*x^4/4 + 36*x^5/5 + 100*x^6/6 + 225*x^7/7 +...+ A001609(n)^2*x^n/n +...
		

Links

• Index entries for linear recurrences with constant coefficients, signature (1, 0, 5, 1, 1, -3, -2, 0, 1).

Crossrefs

Cf. A218439, A001609.

Programs

Mathematica

CoefficientList[Series[1/((1+x^2-x^3)^2(1-x-2x^2-x^3)),{x,0,40}],x] (* or *) LinearRecurrence[{1,0,5,1,1,-3,-2,0,1},{1,1,1,6,12,19,48,110,218},40] (* Harvey P. Dale, Jan 23 2013 *)

PARI

{a(n)=polcoeff(1/((1 + x^2 - x^3)^2*(1 - x*(1+x)^2+x*O(x^n))),n)}
for(n=0,40,print1(a(n),", "))

Formula

Logarithmic derivative yields A218439, where A218439(n) = A001609(n)^2.

a(0)=1, a(1)=1, a(2)=1, a(3)=6, a(4)=12, a(5)=19, a(6)=48, a(7)=110, a(8)=218, a(n)=a(n-1)+5*a(n-3)+a(n-4)+a(n-5)-3*a(n-6)-2*a(n-7)+a(n-9). - Harvey P. Dale, Jan 23 2013