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A090215
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A generalization of triangles A071951 (Legendre-Stirling) and A089504.
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5
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1, 24, 1, 576, 144, 1, 13824, 17856, 504, 1, 331776, 2156544, 199296, 1344, 1, 7962624, 259117056, 73903104, 1328256, 3024, 1, 191102976, 31102009344, 26864234496, 1189638144, 6408576, 6048, 1, 4586471424, 3732432224256
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This triangle underlies the array entry A090214 ((4,4)-generalized Stirling2).
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LINKS
| W. Lang, First 8 rows.
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FORMULA
| G.f. for m-th column sequence (without leading zeros and m>=1) is 1/product(1-fallfac(r+3, 4)*x, r=1..m) with fallfac(n, k) := A008279(n, k) (falling factorials).
a(n, m)=sum(A089515(m, p)*fallfac(p, 4)^(n-m), p=1..m)/D(m) if n>=m>=1 else 0; with D(m) := A089516(m).
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EXAMPLE
| [1]; [24,1]; [576,144,1]; [13824,17856,504,1]; ...
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CROSSREFS
| Cf. A071951 (Legendre-Stirling, (2, 2) case), A089504 ((3, 3)-case).
The column sequences (without leading zeros) are A009968 (powers of 24), etc.
Sequence in context: A103903 A040599 A076721 * A040570 A040569 A040568
Adjacent sequences: A090212 A090213 A090214 * A090216 A090217 A090218
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KEYWORD
| nonn,easy,tabl
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Dec 01 2003
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