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A165618 a(n) = binomial(n+8,8) - 1. 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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).
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.
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 *)
PROG
(PARI) vector(100, n, binomial(n+7, 8)-1) \\ Charles R Greathouse IV, May 27 2011
CROSSREFS
Sequence in context: A000938 A252871 A307044 * A250285 A059596 A327386
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Edited by Charles R Greathouse IV, May 27 2011
STATUS
approved

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Last modified March 29 05:28 EDT 2024. Contains 371264 sequences. (Running on oeis4.)