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 A008500 6-dimensional centered tetrahedral numbers. 2
 1, 8, 36, 120, 330, 792, 1716, 3431, 6427, 11404, 19328, 31494, 49596, 75804, 112848, 164109, 233717, 326656, 448876, 607412, 810510, 1067760, 1390236, 1790643, 2283471, 2885156, 3614248, 4491586, 5540480, 6786900, 8259672 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS If X is an n-set and Y a fixed 7-subset of X then a(n-7) is equal to the number of 7-subsets of X intersecting Y. - Milan Janjic, Jul 30 2007 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Milan Janjic, Two Enumerative Functions Index to sequences with linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1) FORMULA Expansion of (1-x^7)/(1-x)^8 = ( -1-x-x^2-x^3-x^4-x^5-x^6 ) / (x-1)^7. G.f.: (1-x^7)/(1-x)^8. a(-1-n)=a(n). 720*a(n) = 720+1764*n+735*n^3+2128*n^2+385*n^4+21*n^5+7*n^6. - R. J. Mathar, Mar 14 2011 PROG (PARI) a(n)=binomial(n+7, 7)-binomial(n, 7) (MAGMA) [(720 + 1764*n +735*n^3 +2128*n^2 +385*n^4 +21*n^5 + 7*n^6)/720: n in [0..30]]; // Vincenzo Librandi, Oct 08 2011 CROSSREFS Partial sums of A008489. Sequence in context: A014343 A162596 A051192 * A008490 A023033 A000580 Adjacent sequences:  A008497 A008498 A008499 * A008501 A008502 A008503 KEYWORD nonn,easy AUTHOR STATUS approved

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