A221948 Expansion of (x-5*x^2+11*x^3-12*x^4+7*x^5-2*x^6+x^7) / (1-6*x+15*x^2-20*x^3+15*x^4-6*x^5+x^6).

0, 1, 1, 2, 5, 12, 26, 52, 98, 176, 303, 502, 803, 1244, 1872, 2744, 3928, 5504, 7565, 10218, 13585, 17804, 23030, 29436, 37214, 46576, 57755, 71006, 86607, 104860, 126092, 150656, 178932, 211328, 248281, 290258, 337757, 391308, 451474, 518852, 594074, 677808, 770759, 873670, 987323, 1112540, 1250184, 1401160, 1566416, 1746944, 1943781, 2158010

Offset

0,4

Links

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

M. Dairyko, S. Tyner, L. Pudwell and C. Wynn, Non-contiguous pattern avoidance in binary trees, 2012, arXiv:1203.0795 [math.CO], p. 17 (Class D).

Michael Dairyko, Lara Pudwell, Samantha Tyner, Casey Wynn, Non-contiguous pattern avoidance in binary trees. Electron. J. Combin. 19 (2012), no. 3, Paper 22, 21 pp. MR2967227.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

G.f.: x*(1-5*x+11*x^2-12*x^3+7*x^4-2*x^5+x^6)/(1-x)^6.

a(n) = (n-1)*(n^4-14*n^3+111*n^2-354*n+480)/120 for n>1. - Bruno Berselli, Feb 06 2013

Mathematica

CoefficientList[Series[(x - 5 x^2 + 11 x^3 - 12 x^4 + 7 x^5 - 2 x^6 + x^7) / (1 - 6 x + 15 x^2 - 20 x^3 + 15 x^4 - 6 x^5 + x^6), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 19 2013 *)
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 1, 1, 2, 5, 12, 26, 52}, 60] (* Harvey P. Dale, May 07 2018 *)

Crossrefs

Sequence in context: A258099 A132977 A027927 * A116717 A116725 A193263

Adjacent sequences: A221945 A221946 A221947 * A221949 A221950 A221951

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 01 2013

Status

approved