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Search: id:A052250
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| A052250 |
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Triangle T(n,k) (n >= 1, k >= 1) giving dimension of bigrading of Hopf algebra of rooted trees. |
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+0
7
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| 1, 1, 1, 1, 2, 1, 2, 3, 3, 1, 3, 6, 6, 4, 1, 8, 11, 13, 10, 5, 1, 16, 26, 27, 24, 15, 6, 1, 41, 58, 63, 55, 40, 21, 7, 1, 98, 142, 148, 132, 100, 62, 28, 8, 1, 250, 351, 363, 322, 251, 168, 91, 36, 9, 1, 631, 890, 912, 804, 635, 444, 266, 128, 45, 10, 1, 1646, 2282, 2330, 2051
(list; table; graph; listen)
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OFFSET
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0,5
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LINKS
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D. J. Broadhurst and D. Kreimer, Towards cohomology of renormalization...
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EXAMPLE
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1; 1,1; 1,2,1; 2,3,3,1; 3,6,6,4,1; ...
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MAPLE
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with (numtheory): A81:= proc(n) option remember; `if` (n<2, n, (add (add (d*A81(d), d=divisors(j)) *A81(n-j), j=1..n-1))/ (n-1)) end: b:= proc(n) option remember; -`if` (n<0, 1, add (b(n-i) *A81(i+1), i=1..n+1)) end: B:= proc(n) add (b(i) *x^i, i=0..n) end: T:= (n, k)-> coeff (B(n)^k, x, n-k): seq (seq (T(n, k), k=1..n), n=1..13); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 23 2009]
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CROSSREFS
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First few columns give A051573, A051603, A052251, A052252.
Row sums give A000081(n+1). [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 23 2009]
Sequence in context: A057041 A099567 A140530 this_sequence A099569 A097724 A091836
Adjacent sequences: A052247 A052248 A052249 this_sequence A052251 A052252 A052253
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KEYWORD
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nonn,nice,tabl
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AUTHOR
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David Broadhurst (D.Broadhurst(AT)open.ac.uk), Feb 05 2000
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EXTENSIONS
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More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 23 2009
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