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Search: id:A128564
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| A128564 |
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Triangle, read by rows, where T(n,k) equals the number of permutations of {1..n+1} with [(nk+k)/2] inversions for n>=k>=0. |
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+0
5
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| 1, 1, 1, 1, 2, 1, 1, 5, 5, 1, 1, 9, 22, 15, 1, 1, 29, 90, 90, 29, 1, 1, 49, 359, 573, 359, 98, 1, 1, 174, 1415, 3450, 3450, 1415, 174, 1, 1, 285, 5545, 17957, 29228, 21450, 5545, 628, 1, 1, 1068, 21670, 110010, 230131, 230131, 110010, 21670, 1068, 1
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums equal 2*n! for n>0.
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FORMULA
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T(n,k) = A008302(n+1, [(nk+k)/2]) = coefficient of q^[(nk+k)/2] in the q-factorial of n+1 for n>=0.
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EXAMPLE
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Row sums equal 2*n! for n>0:
[1, 2, 4, 12, 48, 240, 1440, 10080, 80640, ..., 2*n!,...].
Triangle begins:
1;
1, 1;
1, 2, 1;
1, 5, 5, 1;
1, 9, 22, 15, 1;
1, 29, 90, 90, 29, 1;
1, 49, 359, 573, 359, 98, 1;
1, 174, 1415, 3450, 3450, 1415, 174, 1;
1, 285, 5545, 17957, 29228, 21450, 5545, 628, 1;
1, 1068, 21670, 110010, 230131, 230131, 110010, 21670, 1068, 1;
1, 1717, 84591, 526724, 1729808, 2409581, 1729808, 686763, 84591, 4015, 1;
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PROGRAM
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(PARI) {T(n, k)=local(faq=prod(j=1, n+1, (1-q^j)/(1-q))); polcoeff(faq, (n*k+k)\2, q)}
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CROSSREFS
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Cf. A008302 (Mahonian numbers); A128565 (column 1), A128566 (column 2).
Adjacent sequences: A128561 A128562 A128563 this_sequence A128565 A128566 A128567
Sequence in context: A139347 A050145 A058676 this_sequence A008518 A139332 A099927
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Mar 12 2007
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