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A145126
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a(n) = 1 + (6 + (11 + (6 + n)*n)*n)*n/24.
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12
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1, 2, 6, 16, 36, 71, 127, 211, 331, 496, 716, 1002, 1366, 1821, 2381, 3061, 3877, 4846, 5986, 7316, 8856, 10627, 12651, 14951, 17551, 20476, 23752, 27406, 31466, 35961, 40921, 46377, 52361, 58906, 66046, 73816, 82252, 91391, 101271, 111931, 123411, 135752
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OFFSET
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0,2
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COMMENTS
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Equals (1, 2, 3, 4, 5, ...) convolved with (1, 0, 3, 6, 10, 15, ...).
Example: a(4) = 36 = (5, 4, 3, 2, 1) dot (1, 0, 3, 6, 10) = (5 + 0 + 9 + 12 + 10). (End)
Also the number of permutations of length n that can be sorted by a single block interchange (in the sense of Christie). - Vincent Vatter, Aug 21 2013
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LINKS
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FORMULA
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G.f.: (x^4-4*x^3+6*x^2-3*x+1) / (1-x)^5.
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MAPLE
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a:= n-> 1+ (6+ (11+ (6+ n) *n) *n) *n/24: seq(a(n), n=0..40);
# second Maple program:
with(combinat): seq(binomial(n+3, 4)+1, n=0..40); # Zerinvary Lajos, Mar 24 2009
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MATHEMATICA
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CoefficientList[Series[(x^4 - 4 x^3 + 6 x^2 - 3 x + 1) / (1 - x)^5, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 06 2013 *)
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PROG
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(PARI) Vec((x^4-4*x^3+6*x^2-3*x+1)/(1-x)^5 + O(x^50)) \\ Altug Alkan, Nov 24 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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