A098478 Expansion of 1/sqrt(1-2x-11x^2+12x^3).

1, 1, 7, 13, 73, 187, 895, 2737, 11923, 40333, 166753, 598111, 2404309, 8926651, 35365651, 134054005, 527360581, 2024611351, 7940840719, 30733601689, 120439122811, 468630460885, 1836912780541, 7173754477099, 28140632060899

Offset

0,3

Comments

1/sqrt(1-2x-(4r-1)x^2+4r^3) expands to give sum{k=0..floor(n/2), binomial(2k,k)binomial(n-k,n-2k)r^k}.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(n)=sum{k=0..floor(n/2), binomial(2k, k)binomial(n-k, n-2k)3^k}.

D-finite with recurrence: n*a(n) = (2*n-1)*a(n-1) + 11*(n-1)*a(n-2) - 6*(2*n-3)*a(n-3). - Vaclav Kotesovec, Jun 23 2014

a(n) ~ 2^(2*n+2) / sqrt(21*Pi*n). - Vaclav Kotesovec, Jun 23 2014

Mathematica

CoefficientList[Series[1/Sqrt[1-2*x-11*x^2+12*x^3], {x, 0, 20}], x] (* Vaclav Kotesovec, Jun 23 2014 *)

Crossrefs

Cf. A026569, A098477.

Sequence in context: A159198 A106976 A219908 * A174878 A177198 A177163

Adjacent sequences: A098475 A098476 A098477 * A098479 A098480 A098481

Keyword

nonn

Author

Paul Barry, Sep 10 2004

Status

approved