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 A128888 Table with g.f. [1-x*n-sqrt(x^2*n^2-2*n*x+1+4*x^2-4*x)]/(2*x). 0
 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; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS 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. LINKS EXAMPLE 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,... MAPLE 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; CROSSREFS Cf. A005563, A002212, A129170. Sequence in context: A055137 A143325 A307910 * A305401 A306100 A294046 Adjacent sequences:  A128885 A128886 A128887 * A128889 A128890 A128891 KEYWORD easy,nonn,tabl AUTHOR R. J. Mathar, Apr 19 2007 STATUS approved

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Last modified May 31 16:29 EDT 2020. Contains 334748 sequences. (Running on oeis4.)