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Search: id:A089504
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| A089504 |
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A generalization of triangle A071951 (Legendre-Stirling). |
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+0
10
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| 1, 6, 1, 36, 30, 1, 216, 756, 90, 1, 1296, 18360, 6156, 210, 1, 7776, 441936, 387720, 31356, 420, 1, 46656, 10614240, 23705136, 4150440, 119556, 756, 1, 279936, 254788416, 1432922400, 521757936, 29257200, 373572, 1260, 1, 1679616
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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This triangle underlies the array entry A078741 ((3,3)-generalized Stirling2).
For the computation of the column sequences see A089505.
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LINKS
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W. Lang, First 8 rows.
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FORMULA
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G.f. for m-th column sequence (without leading zeros and m>=1) is 1/product(1-fallfac(r+2, 3)*x, r=1..m) with fallfac(n, k) := A008279(n, k) (falling factorials).
a(n, m)=sum(A089505(m, p)*((p+2)*(p+1)*p)^(n-m), p=1..m)/D(m) if n>=m>=1 else 0; with D(m) := A089506(m).
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EXAMPLE
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[1]; [6,1]; [36,30,1]; [216,756,90,1]; ...
a(3,2) = 30 = ((-1)*(3*2*1)^1 + 4*(4*3*2)^1)/3.
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CROSSREFS
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Cf. A071951 (Legendre-Stirling, (2, 2) case).
The column sequences (without leading zeros) are A000400 (powers of 6), A089507, A089513-4, etc.
Sequence in context: A147320 A038255 A075501 this_sequence A145927 A113365 A145356
Adjacent sequences: A089501 A089502 A089503 this_sequence A089505 A089506 A089507
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Dec 01 2003
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