A027967 T(n, 2*n-5), T given by A027960.

3, 7, 18, 44, 98, 199, 373, 654, 1085, 1719, 2620, 3864, 5540, 7751, 10615, 14266, 18855, 24551, 31542, 40036, 50262, 62471, 76937, 93958, 113857, 136983, 163712, 194448, 229624, 269703, 315179, 366578, 424459, 489415, 562074, 643100, 733194, 833095, 943581, 1065470, 1199621

Offset: 3

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• G. C. Greubel, 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

A column of triangle A027011.

Programs

GAP

List([3..50], n-> (840-736*n+300*n^2-45*n^3+n^5)/120) G. C. Greubel, Jun 30 2019

Magma

[(840-736*n+300*n^2-45*n^3+n^5)/120: n in [3..50]]; // G. C. Greubel, Jun 30 2019

Mathematica

LinearRecurrence[{6,-15,20,-15,6,-1}, {3,7,18,44,98,199}, 50] (* G. C. Greubel, Jun 30 2019 *)

PARI

for(n=3,50, print1((840-736*n+300*n^2-45*n^3+n^5)/120, ", ")) \\ G. C. Greubel, Jun 30 2019

Sage

[(840-736*n+300*n^2-45*n^3+n^5)/120 for n in (3..50)] # G. C. Greubel, Jun 30 2019

Formula

From Ralf Stephan, Feb 07 2004: (Start)

G.f.: x^3*(3-2*x)*(1-3*x+5*x^2-3*x^3+x^4)/(1-x)^6.

Differences of A027968. (End)

From G. C. Greubel, Jun 30 2019: (Start)

a(n) = (840 - 736*n + 300*n^2 - 45*n^3 + n^5)/120.

E.g.f.: (-120*(7 + 3*x + x^2) + (840 - 480*x + 180*x^2 - 20*x^3 + 10*x^4 + x^5)*exp(x))/120. (End)

Extensions

Terms a(37) onward added by G. C. Greubel, Jun 30 2019