A135925 G.f.: (x^2+x-1)*(1+2*x+S)*(1-5*x+2*x^2+(3*x-1)*S)^2*(-1+3*x+2*x^2+(1-x)*S), where S=sqrt(1-4*x).

0, 0, 0, 0, 0, 0, -16, 0, 80, 240, 656, 1936, 6000, 19088, 61792, 202832, 673888, 2263392, 7677712, 26280800, 90709616, 315486768, 1104982560, 3895248720, 13813470240, 49256281920, 176536299168, 635710344672, 2299280127328, 8350257302304, 30441306959040

Offset

0,7

References

C. K. Fan, Structure of a Hecke algebra quotient, J. Amer. Math. Soc., 10 (1997), 139-167. [See D(y) on p. 158.]

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

a(n) ~ 11*2^(2*n-13)/(sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 29 2013

Conjecture D-finite with recurrence: +4*(n-1)*(7678757997599*n-100709801435251)*a(n) +(-291262905844111*n^2+4745710679447853*n-12935393149282124)*a(n-1) +3*(268523622217993*n^2-4978734571371597*n+20251709258114720)*a(n-2) +2*(-196528865827703*n^2+4147266222561252*n-21888137659762186)*a(n-3) -12*(22463548140013*n-247087251730058)*(2*n-25)*a(n-4)=0. - R. J. Mathar, Jan 23 2020

Maple

S:=sqrt(1-4*y); Dy:=(y^2+y-1)*(1+2*y+S)*(1-5*y+2*y^2+(3*y-1)*S)^2*(-1+3*y+2*y^2+(1-y)*S);

Mathematica

CoefficientList[Series[(x^2 + x - 1) (1 + 2 x + Sqrt[1 - 4 x]) (1 - 5 x + 2 x^2 + (3 x - 1) Sqrt[1 - 4 x])^2 (-1 + 3 x + 2 x^2 + (1 - x) Sqrt[1 - 4 x]), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 30 2016 *)

Crossrefs

Cf. A135926.

Sequence in context: A059060 A331140 A059681 * A188784 A123935 A169764

Adjacent sequences: A135922 A135923 A135924 * A135926 A135927 A135928

Keyword

sign

Author

N. J. A. Sloane, Mar 09 2008

Status

approved