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A096942 Fifth column of (1,5)-Pascal triangle A096940. 3
5, 21, 55, 115, 210, 350, 546, 810, 1155, 1595, 2145, 2821, 3640, 4620, 5780, 7140, 8721, 10545, 12635, 15015, 17710, 20746, 24150, 27950, 32175, 36855, 42021, 47705, 53940, 60760, 68200, 76296, 85085, 94605, 104895, 115995, 127946, 140790, 154570 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
If Y is a 5-subset of an n-set X then, for n>=8, a(n-8) is the number of 4-subsets of X having at most one element in common with Y. - Milan Janjic, Dec 08 2007
LINKS
FORMULA
a(n) = (n+20)*binomial(n+3, 3)/4 = 5*b(n) - 4*b(n-1), with b(n) = A000332(n+4) = binomial(n+4, 4).
G.f.: (5-4*x)/(1-x)^5.
a(n) = sum_{k=1..n} (sum_{i=1..k) i*(n-k+5)). - Wesley Ivan Hurt, Sep 26 2013
MATHEMATICA
Table[(n + 20) Binomial[n + 3, 3]/4, {n, 0, 100}]
CoefficientList[Series[(5 - 4 x)/(1 - x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Oct 01 2013 *)
PROG
(Magma) [(n + 20)*Binomial(n + 3, 3) div 4: n in [0..50]]; // Vincenzo Librandi, Oct 01 2013
CROSSREFS
Fourth column: A096941; sixth column: A096943.
Sequence in context: A147834 A160378 A201440 * A365300 A122244 A146854
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jul 16 2004
STATUS
approved

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Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)