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

0,2

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R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]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).

Formula

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

Prog

(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

Crossrefs

Sequence in context: A099193 A086951 A041370 * A055913 A283805 A005757

Adjacent sequences: A244880 A244881 A244882 * A244884 A244885 A244886

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 08 2014

Status

approved