A259563 a(n) = 81*n^3*(n-1)^5*(n+1)^2*(n^2-6*n+1)*(n^3-79*n^2+163*n-81).

0, 0, 2571912, 2472394752, 138662798400, 1666179072000, -4637478825000, -272992368918528, -3187483870330368, -23209723979366400, -126970182577359000, -566493158246400000, -2161675076294530368, -7278963158259007488, -22112928086617859400, -61611251010011136000

Offset: 0

Author

Vincenzo Librandi, Jun 30 2015

Keywords

• sign
• easy

Links

• M. P. Delest, Generating functions for column-convex polyominoes, J. Combin. Theory Ser. A 48 (1988), no. 1, pp. 12-31. See expression F in Theorem 16 page 29.
• 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).

Crossrefs

Cf. A001105, A005435, A259364, A259395, A259435.

Programs

Magma

[81*n^3*(n-1)^5*(n+1)^2*(n^2-6*n+1)*(n^3-79*n^2+163*n-81): n in [0..20]];

Mathematica

Table[81 n^3 (n-1)^5 (n+1)^2 (n^2 - 6 n + 1) (n^3 - 79 n^2 + 163 n - 81), {n, 0, 23}]
LinearRecurrence[{16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1},{0,0,2571912,2472394752,138662798400,1666179072000,-4637478825000,-272992368918528,-3187483870330368,-23209723979366400,-126970182577359000,-566493158246400000,-2161675076294530368,-7278963158259007488,-22112928086617859400,-61611251010011136000},20] (* Harvey P. Dale, Sep 02 2024 *)

Formula

G.f.: 52488*x^2*(49 + 46320*x + 1894016*x^2 - 4899760*x^3 - 305530185*x^4 - 1372006208*x^5 - 1287460720*x^6 + 1418574528*x^7 + 2422309735*x^8 + 1000206160*x^9 + 139190784*x^10 + 5654000*x^11 + 37281*x^12)/(1-x)^16.

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).