A027969 a(n) = T(n, 2*n-7), T given by A027960.

3, 7, 18, 47, 120, 291, 661, 1404, 2801, 5283, 9484, 16305, 26990, 43215, 67191, 101782, 150639, 218351, 310614, 434419, 598260, 812363, 1088937, 1442448, 1889917, 2451243, 3149552, 4011573, 5068042, 6354135, 7909931, 9780906, 12018459, 14680471, 17831898, 21545399, 25902000, 30991795

Offset: 4

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 4..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

A column of triangle A027011.

Programs

GAP

List([4..50], n-> (90720 -85548*n +38822*n^2 -10136*n^3 +1505*n^4 -77*n^5 -7*n^6 + n^7)/5040) # G. C. Greubel, Jul 01 2019

Magma

[(90720 -85548*n +38822*n^2 -10136*n^3 +1505*n^4 -77*n^5 -7*n^6 + n^7)/5040: n in [4..50]]; // G. C. Greubel, Jul 01 2019

Mathematica

Table[(90720 -85548*n +38822*n^2 -10136*n^3 +1505*n^4 -77*n^5 -7*n^6 + n^7)/5040, {n,4,50}] (* G. C. Greubel, Jul 01 2019 *)

PARI

for(n=4,50, print1((90720 -85548*n +38822*n^2 -10136*n^3 +1505*n^4 -77*n^5 -7*n^6 + n^7)/5040, ", ")) \\ G. C. Greubel, Jul 01 2019

Sage

[(90720 -85548*n +38822*n^2 -10136*n^3 +1505*n^4 -77*n^5 -7*n^6 + n^7)/5040 for n in (4..50)] # G. C. Greubel, Jul 01 2019

Formula

From Ralf Stephan, Feb 07 2004: (Start)

G.f.: x^4*(3-2x)*(1-x+x^2)*(1-4x+7x^2-4x^3+x^4)/(1-x)^8.

First differences of A027970. (End)

From G. C. Greubel, Jul 01 2019: (Start)

a(n) = (90720 -85548*n +38822*n^2 -10136*n^3 +1505*n^4 -77*n^5 -7*n^6 + n^7)/5040.

E.g.f.: (-90720 - 35280*x - 7560*x^2 - 1680*x^3 + (90720 - 55440*x + 17640*x^2 - 3360*x^3 + 630*x^4 - 42*x^5 + 14*x^6 + x^7)*exp(x))/5040. (End)

Extensions

Terms a(35) onward added by G. C. Greubel, Jul 01 2019