A129148 Expansion of (1-x-sqrt(1-6*x-7*x^2))/(2*(1+2*x)).

1, 2, 8, 36, 180, 956, 5300, 30316, 177604, 1060284, 6427092, 39452364, 244748196, 1532044572, 9664688436, 61380865452, 392148430212, 2518518772604, 16250624534420, 105297028489612, 684865176181348

Offset

1,2

Comments

Series reversion of x(1-x)/(1+x+2x^2).

Hankel transform is 4^C(n+1,2)=A053763(n+1).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Formula

a(n)=sum{k=0..n, sum{j=0..n, C(n,j)*C(n-k,j+k-n)*C(n-k)*3^(j+k-n)}}, C(n)=A000108(n); a(n)=(1/(2*pi))*int(x^n*sqrt(7+6*x-x^2)/(2+x),x,-1,7);

D-finite with recurrence: n*a(n) = (4*n-9)*a(n-1) + (19*n-39)*a(n-2) + 14*(n-3)*a(n-3) . - Vaclav Kotesovec, Oct 20 2012

a(n) ~ 7^(n+1/2)/(9*sqrt(2*Pi)*n^(3/2)) . - Vaclav Kotesovec, Oct 20 2012

Mathematica

Rest[CoefficientList[Series[(1-x-Sqrt[1-6*x-7*x^2])/(2*(1+2*x)), {x, 0, 20}], x]] (* Vaclav Kotesovec, Oct 20 2012 *)
Table[(1/(2*Pi))*Integrate[x^n*Sqrt[7+6*x-x^2]/(2+x), {x, -1, 7}], {n, 0, 10}] (* Vaclav Kotesovec, Oct 20 2012 *)

Crossrefs

Sequence in context: A113327 A227791 A245102 * A285672 A081958 A369619

Adjacent sequences: A129145 A129146 A129147 * A129149 A129150 A129151

Keyword

easy,nonn

Author

Paul Barry, Apr 01 2007

Extensions

Offset corrected to 1, Vaclav Kotesovec, Oct 20 2012

Status

approved