A244883 Expansion of (1+6*x+16*x^2+8*x^3+x^4)/(1-x)^8.

1, 14, 100, 472, 1691, 4988, 12744, 29160, 61149, 119482, 220220, 386464, 650455, 1056056, 1661648, 2543472, 3799449, 5553510, 7960468, 11211464, 15540019, 21228724, 28616600, 38107160, 50177205, 65386386, 84387564, 107938000, 136911407, 172310896, 215282848

Offset: 0

Author

N. J. A. Sloane, Jul 08 2014

Keywords

• nonn
• easy

Links

• Todd Silvestri, Table of n, a(n) for n = 0..10000
• R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Programs

Magma

[((n+1)*(n+2)*(n+3)*(n*(n+4)*(n*(16*n+57)+137)+420))/2520: n in [0..40]]; // Vincenzo Librandi, Nov 16 2014

Mathematica

a[n_Integer/;n>=0]:=((n+1) (n+2) (n+3) (n (n+4) (n (16 n+57)+137)+420))/2520 (* Todd Silvestri, Nov 16 2014 *)
CoefficientList[Series[(1 + 6 x + 16 x^2 + 8 x^3 + x^4) / (1 - x)^8, {x, 0, 100}], x] (* Vincenzo Librandi, Nov 16 2014 *)
LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{1,14,100,472,1691,4988,12744,29160},40] (* Harvey P. Dale, May 11 2020 *)

Formula

a(n) = ((n+1)*(n+2)*(n+3)*(n*(n+4)*(n*(16*n+57)+137)+420))/2520. - Todd Silvestri, Nov 16 2014