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Search: id:A089503
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| A089503 |
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Triangle of numbers used for basis change between certain falling factorials. |
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+0
2
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| 1, 1, 4, 1, 12, 30, 1, 24, 168, 336, 1, 40, 540, 2880, 5040, 1, 60, 1320, 13200, 59400, 95040, 1, 84, 2730, 43680, 360360, 1441440, 2162160, 1, 112, 5040, 117600, 1528800, 11007360, 40360320, 57657600, 1, 144, 8568, 274176, 5140800, 57576960
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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Used to relate array A078739 ((2,2)-Stirling2) to triangle A071951 (Legendre-Stirling).
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LINKS
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W. Lang, First 9 rows.
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FORMULA
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fallfac(x+n-1, 2*n) = sum(a(n, m)*fallfac(x, 2*n-(m-1)), m=1..n), n>=1, and with fallfac(x, k) := product(x+1-j, j=1..k), with fallfac(n, k)=A068424(n, k) (falling factorials). a(n, m)=0 if n < m.
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EXAMPLE
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1; 1,4; 1,12,30; 1,24,168,336; ...
n=3: fallfac(x+2,6) = 1*fallfac(x,6) + 12*fallfac(x,5) + 30*fallfac(x,4).
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CROSSREFS
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Sequence in context: A078219 A117413 A105197 this_sequence A019236 A019237 A019238
Adjacent sequences: A089500 A089501 A089502 this_sequence A089504 A089505 A089506
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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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