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

Author

Clark Kimberling

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A228074, A000045.

Programs

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

Magma

[(n-2)*(n^4-8*n^3+39*n^2-92*n+180)/120: n in [3..40]]; // Vincenzo Librandi, Apr 22 2012

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 *)

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

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