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Search: id:A128888
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| A128888 |
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Table with g.f. [1-x*n-sqrt(x^2*n^2-2*n*x+1+4*x^2-4*x)]/(2*x). |
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1
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| 1, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 3, 8, 10, 0, 1, 4, 15, 36, 36, 0, 1, 5, 24, 84, 176, 137, 0, 1, 6, 35, 160, 510, 912, 543, 0, 1, 7, 48, 270, 1152, 3279, 4928, 2219, 0, 1, 8, 63, 420, 2240, 8768, 21975, 27472, 9285, 0, 1, 9, 80, 616, 3936, 19605, 69504, 151905, 156864
(list; table; graph; listen)
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OFFSET
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0,8
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COMMENT
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Column m=2 is essentially the same as A005563 or A067998 or A106230. Row n=1 is essentially the same as A025238 and A002212. The table is read along diagonals and provides the Taylor coefficient of x^m in column m. It also is the slice t=1 through the trivariate g.f. defined in A129170, which provides an implicit proof that all values are nonnegative.
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EXAMPLE
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Table with rows n>=0 and columns m>=0 starts
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
1, 1, 3, 10, 36, 137, 543, 2219, 9285, 39587, 171369, ...
1, 2, 8, 36, 176, 912, 4928, 27472, 156864, 912832, 5394176, ...
1, 3, 15, 84, 510, 3279, 21975, 151905, 1075425, 7758777, 56839965, ...
1, 4, 24, 160, 1152, 8768, 69504, 568064, 4753920, 40537088, 350963712, ...
1, 5, 35, 270, 2240, 19605, 178535, 1675495, 16095765, 157527055, 1565170985, ...
1, 6, 48, 420, 3936, 38832, 398208, 4205904, 45459840, 500488512, 5593373184, ...
1, 7, 63, 616, 6426, 70427, 801423, 9387917, 112501809, 1372985957, 17007257421,...
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MAPLE
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H := proc(n, x) (-x*n+1-(x^2*n^2-2*n*x+1+4*x^2-4*x)^(1/2))/(2*x) ; end: T := proc(n, m) coeftayl( H(n, x), x=0, m) ; end: for diag from 0 to 20 do for m from 0 to diag do n := diag-m ; printf("%d, ", T(n, m)) ; od ; od;
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CROSSREFS
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Cf. A005563, A002212, A129170.
Sequence in context: A072516 A106450 A055137 this_sequence A004443 A008290 A059066
Adjacent sequences: A128885 A128886 A128887 this_sequence A128889 A128890 A128891
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 19 2007
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