A259435 a(n) = 2*(n-1)^6*(n+1)^2*(n^2+10*n+1).

2, 0, 450, 81920, 2077650, 22413312, 148531250, 716636160, 2763575010, 9017753600, 25850353122, 66816000000, 158678718770, 351151718400, 731985584850, 1449526034432, 2745436781250, 5000952545280, 8800799033090, 15019798118400, 24938174692242, 40392704000000

Offset: 0

Author

Vincenzo Librandi, Jun 27 2015

Keywords

• nonn
• easy

Comments

This appears as the function alpha(n) in Delest, related to bar/bat theory; see section 3.

Links

• M. P. Delest, Generating functions for column-convex polyominoes, J. Combin. Theory Ser. A 48 (1988), no. 1, pp. 12-31. See expression E in Theorem 16 page 29.
• Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Crossrefs

Cf. A001105, A005435, A259364, A259395.

Programs

Magma

[2*(n-1)^6*(n+1)^2*(n^2+10*n+1): n in [0..30]];

Maple

A259435:=n->2*(n-1)^6*(n+1)^2*(n^2+10*n+1): seq(A259435(n), n=0..30); # Wesley Ivan Hurt, Jun 29 2015

Mathematica

Table[2 (n - 1)^6 (n + 1)^2 (n^2 + 10 n + 1), {n, 0, 30}]
LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{2,0,450,81920,2077650,22413312,148531250,716636160,2763575010,9017753600,25850353122},30] (* Harvey P. Dale, Dec 29 2024 *)

PARI

a(n)=2*(n-1)^6*(n+1)^2*(n^2+10*n+1) \\ Charles R Greathouse IV, Jun 29 2015

Sage

[2*(n-1)^6*(n+1)^2*(n^2+10*n+1) for n in (0..30)] # Bruno Berselli, Jun 30 2015

Formula

G.f.: 2*(1 -11*x + 280*x^2 + 38320*x^3 + 600970*x^4 + 1994794*x^5 + 1444096*x^6 - 231320*x^7 - 207395*x^8 - 10935*x^9)/(1-x)^11.

a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11).