A027928 a(n) = T(n, 2*n-5), T given by A027926.

1, 3, 8, 20, 46, 97, 189, 344, 591, 967, 1518, 2300, 3380, 4837, 6763, 9264, 12461, 16491, 21508, 27684, 35210, 44297, 55177, 68104, 83355, 101231, 122058, 146188, 174000, 205901, 242327, 283744, 330649, 383571, 443072

Offset

3,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 3..1000

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

a(n) = (n-2)*(n^4 - 8*n^3 + 39*n^2 - 92*n + 180)/120.

a(n) = C(n,n-1) + C(n+1,n-2) + C(n+2,n-3) with offset 1. - Zerinvary Lajos, May 29 2007

G.f.: x^3*(1 - 3*x + 5*x^2 - 3*x^3 + x^4)/(1-x)^6. - Colin Barker, Mar 18 2012

E.g.f.: 3 + x -(360 - 240*x + 60*x^2 - 20*x^3 - x^5)*exp(x)/120. - G. C. Greubel, Sep 06 2019

Maple

seq(binomial(n, n-1)+binomial(n+1, n-2)+binomial(n+2, n-3), n=1..35); # Zerinvary Lajos, May 29 2007

Mathematica

CoefficientList[Series[(1-3*x+5*x^2-3*x^3+x^4)/(1-x)^6, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 22 2012 *)

Prog

(Magma) [(n-2)*(n^4-8*n^3+39*n^2-92*n+180)/120: n in [3..40]]; // Vincenzo Librandi, Apr 22 2012
(PARI) vector(40, n, m=n+2; n*(m^4 -8*m^3 +39*m^2 -92*m +180)/120) \\ G. C. Greubel, Sep 06 2019
(Sage) [(n-2)*(n^4 -8*n^3 +39*n^2 -92*n +180)/120 for n in (3..40)] # G. C. Greubel, Sep 06 2019
(GAP) List([3..40], n-> (n-2)*(n^4 -8*n^3 +39*n^2 -92*n +180)/120); # G. C. Greubel, Sep 06 2019

Crossrefs

Cf. A228074, A000045.

Sequence in context: A034504 A191522 A140481 * A026624 A026690 A036676

Adjacent sequences: A027925 A027926 A027927 * A027929 A027930 A027931

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved