A158501 Hankel transform of A158500.

1, 0, 25, -24, 105, -104, 273, -272, 561, -560, 1001, -1000, 1625, -1624, 2465, -2464, 3553, -3552, 4921, -4920, 6601, -6600, 8625, -8624, 11025, -11024, 13833, -13832, 17081, -17080, 20801, -20800, 25025, -25024, 29785, -29784, 35113, -35112, 41041, -41040

Offset

0,3

Links

Colin Barker, Table of n, a(n) for n = 0..1000

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

Formula

G.f.: (1+x+22*x^2-2*x^3+9*x^4+x^5) / ((1-x)^3*(1+x)^4).

a(n) = -a(n-1)+3*a(n-2)+3*a(n-3)-3*a(n-4)-3*a(n-5)+a(n-6)+a(n-7).

From Colin Barker, Jan 29 2016: (Start)

a(n) = (n+1)*(2*(-1)^n*n^2+4*(-1)^n*n+3*n+3)/3.

a(n) = (2*n^3+9*n^2+10*n+3)/3 for n even.

a(n) = (-2*n^3-3*n^2+2*n+3)/3 for n odd.

(End)

Mathematica

LinearRecurrence[{-1, 3, 3, -3, -3, 1, 1}, {1, 0, 25, -24, 105, -104, 273}, 40] (* Harvey P. Dale, Aug 19 2012 *)

Prog

(PARI) Vec((1+x+22*x^2-2*x^3+9*x^4+x^5)/((1-x)^3*(1+x)^4) + O(x^50)) \\ Colin Barker, Jan 29 2016

Crossrefs

Sequence in context: A061438 A022981 A023467 * A330272 A194219 A291434

Adjacent sequences: A158498 A158499 A158500 * A158502 A158503 A158504

Keyword

easy,sign

Author

Paul Barry, Mar 20 2009

Status

approved