A272765 Expansion of (1 + 80*x + 2592*x^2 + 29360*x^3 + 138124*x^4 + 295552*x^5 + 299984*x^6 + 144016*x^7 + 31146*x^8 + 2688*x^9 + 72*x^10)/(1-x)^16.

1, 96, 4008, 82528, 1029552, 8939152, 59112616, 316345408, 1429655844, 5627681904, 19747867728, 62882889360, 184259252180, 502404837648, 1286281062776, 3115358788304, 7182265229303, 15843826126704, 33591306176240, 68708263470288, 136027864081380

Offset

0,2

Comments

Values of Ehrhart polynomial for a facet of the Birkhoff polytope B_5.

Linear recurrence signature is given by (-1)^n*binomial(16,n+1) for n=0..15. - Bruno Berselli, May 07 2016

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Jesús A. De Loera, Fu Liu, and Ruriko Yoshida, A generating function for all semi-magic squares and the volume of the Birkhoff polytope, J. Algebraic Combin. 30 (2009), no. 1 (see table on page 137, 3rd row).

Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).

Formula

G.f.: (1 + 80*x + 2592*x^2 + 29360*x^3 + 138124*x^4 + 295552*x^5 + 299984*x^6 + 144016*x^7 + 31146*x^8 + 2688*x^9 + 72*x^10)/(1 - x)^16.

a(n) = (1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)*(2179457280 + 5624791200*n + 8463690360*n^2 + 8430731628*n^3 + 5888536294*n^4 + 2935665243*n^5 + 1043021847*n^6 + 258468462 n^7 + 42566616*n^8 + 4198827*n^9 + 188723*n^10)/261534873600.

a(n) = 16*a(n-1) - 120*a(n-2) + 560*a(n-3) - 1820*a(n-4) + 4368*a(n-5) - 8008*a(n-6) + 11440*a(n-7) - 12870*a(n-8) + 11440*a(n-9) - 8008*a(n-10) + 4368*a(n-11) - 1820*a(n-12) + 560*a(n-13) - 120*a(n-14) + 16*a(n-15) - a(n-16). - Wesley Ivan Hurt, Jul 02 2020

Mathematica

CoefficientList[Series[(1 + 80 x + 2592 x^2 + 29360 x^3 + 138124 x^4 + 295552 x^5 + 299984 x^6 + 144016 x^7 + 31146 x^8 + 2688 x^9 + 72 x^10)/(1 - x)^16, {x, 0, 20}], x]

Prog

(PARI) Vec((1 + 80*x + 2592*x^2 + 29360*x^3 + 138124*x^4 + 295552*x^5 + 299984*x^6 + 144016*x^7 + 31146*x^8 + 2688*x^9 + 72*x^10)/(1 - x)^16 + O(x^21))
(Magma) m:=21; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1 + 80*x + 2592*x^2 + 29360*x^3 + 138124*x^4 + 295552*x^5 + 299984*x^6 + 144016*x^7 + 31146*x^8 + 2688*x^9 + 72*x^10)/(1 - x)^16));

Crossrefs

Cf. A271899.

Sequence in context: A282210 A008660 A164751 * A240445 A229458 A285171

Adjacent sequences: A272762 A272763 A272764 * A272766 A272767 A272768

Keyword

nonn,easy

Author

Vincenzo Librandi, May 06 2016

Extensions

Edits, programs, new definition by Bruno Berselli, May 07 2016

Status

approved