A165618 a(n) = binomial(n+8,8) - 1.

0, 8, 44, 164, 494, 1286, 3002, 6434, 12869, 24309, 43757, 75581, 125969, 203489, 319769, 490313, 735470, 1081574, 1562274, 2220074, 3108104, 4292144, 5852924, 7888724, 10518299, 13884155, 18156203, 23535819, 30260339, 38608019, 48903491

Offset: 0

Author

Enrique Pérez Herrero, Sep 22 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• E. Pérez Herrero, Binomial Matrix (I) partitions, Psychedelic Geometry Blogspot, 09/22/09
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Cf. A000096, A000581, A062748, A063258, A062988, A124089, A124090, A035927.

Programs

Mathematica

Table[ -1 + Binomial[n + 8, 8], {n, 0, 30}]
LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{0,8,44,164,494,1286,3002,6434,12869},40] (* Harvey P. Dale, Nov 18 2013 *)

PARI

vector(100,n,binomial(n+7,8)-1) \\ Charles R Greathouse IV, May 27 2011

Formula

a(n) = binomial(n+8,8) - 1 = A000581(n+8) - 1.

a(n) = Sum_{r=1..n} binomial(8,r)*binomial(n,r).

a(n) = n(n+9)(n^6 + 27n^5 + 303n^4 + 1809n^3 + 6168n^2 + 11772n + 12176)/40320.

Extensions

Edited by Charles R Greathouse IV, May 27 2011