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Search: id:A165675
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| A165675 |
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Extended triangle related to the asymptotic expansions of the E(x,m=2,n) |
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6
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| 1, 1, 1, 2, 3, 1, 6, 11, 5, 1, 24, 50, 26, 7, 1, 120, 274, 154, 47, 9, 1, 720, 1764, 1044, 342, 74, 11, 1, 5040, 13068, 8028, 2754, 638, 107, 13, 1, 40320, 109584, 69264, 24552, 5944, 1066, 146, 15, 1
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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This triangle is the same as triangle A165674 except for the extra left hand column a(n,0) = n!. The a(n) formulae for the right hand columns generate the coefficients of this extra left hand column, see A080663, A165676, A165677, A165678 and A165679.
Leroy Quet discovered triangle A105954 which is the reversal of our triangle.
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FORMULA
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a(n,m) = (n-m+1)*a(n-1,m) + a(n-1,m-1), 1 =< m =< n-1, with a(n,m=0) = n! and a(n,n) = 1.
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MAPLE
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nmax:=9; for n from 0 to nmax do a(n, 0):= n! od: for n from 0 to nmax do a(n, n):=1 od: for n from 2 to nmax do for m from 1 to n-1 do a(n, m):=(n-m+1)*a(n-1, m)+a(n-1, m-1) od: od: T:=0: for n from 0 to nmax do for m from 0 to n do a(T):=a(n, m): T:=T+1: od: od: seq(a(n), n=0..T-1);
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CROSSREFS
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A105954 is the reversal of this triangle.
A165674, A138771 and A165680 are related triangles.
A080663 equals the third right hand column.
A000142 equals the first left hand column.
A093345 are the row sums.
Sequence in context: A103136 A155856 A086960 this_sequence A138771 A121748 A008275
Adjacent sequences: A165672 A165673 A165674 this_sequence A165676 A165677 A165678
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 05 2009
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