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Search: id:A104035
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| A104035 |
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Triangle T(n,k), 0<=k<=n, read by rows, defined by T(0,0) = 1; T(0,k) = 0 if k>0 or if k<0; T(n,k) = k*T(n-1,k-1) + (k+1)*T(n-1,k+1). |
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+0
3
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| 1, 0, 1, 1, 0, 2, 0, 5, 0, 6, 5, 0, 28, 0, 24, 0, 61, 0, 180, 0, 120, 61, 0, 662, 0, 1320, 0, 720, 0, 1385, 0, 7266, 0, 10920, 0, 5040, 1385, 0, 24568, 0, 83664, 0, 100800, 0, 40320, 0, 50521, 0, 408360, 0, 1023120, 0, 1028160, 0, 362880, 50521, 0, 1326122, 0, 6749040
(list; table; graph; listen)
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OFFSET
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0,6
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COMMENT
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Triangle related to Euler and Springer numbers.
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REFERENCES
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S. Mukai, An Introduction to Invariants and Moduli, Cambridge, 2003; see pp. 445 and 469.
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FORMULA
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T(n, n) = n!; T(n, 0) = 0 if n = 2m + 1; T(n, 0) = A000364(m) if n = 2m.
Sum_{k>=0} T(m, k)*T(n, k) = T(m+n, 0).
Sum_{k>=0} T(n, k) = A001586(n): Springer numbers.
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EXAMPLE
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Triangle begins:
1
0 1
1 0 2
0 5 0 6
5 0 28 0 24
0 61 0 180 0 120
61 0 662 0 1320 0 720
0 1385 0 7266 0 10920 0 5040
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CROSSREFS
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Cf. A000364 A001586.
Sequence in context: A054013 A048050 A078153 this_sequence A115333 A105523 A126120
Adjacent sequences: A104032 A104033 A104034 this_sequence A104036 A104037 A104038
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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Philippe DELEHAM ( kolotoko(AT)wanadoo.fr), Apr 06 2005
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