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Search: id:A134275
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| A134275 |
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Triangle of numbers obtained from the partition array A134274. |
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+0
5
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| 1, 5, 1, 45, 5, 1, 585, 70, 5, 1, 9945, 810, 70, 5, 1, 208845, 14895, 935, 70, 5, 1, 5221125, 284895, 16020, 935, 70, 5, 1, 151412625, 7055100, 309645, 16645, 935, 70, 5, 1, 4996616625, 192734100, 7526475, 315270, 16645, 935, 70, 5, 1, 184874815125
(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 is named S2(5)'.
In the same manner the unsigned Lah triangle A008297 is obtained from the partition array A130561.
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LINKS
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W. Lang, First 10 rows and more.
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FORMULA
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a(n,m)=sum(product(S2(5;j,1)^e(n,m,q,j),j=1..n),q=1..p(n,m)) if n>=m>=1, else 0. Here p(n,m)=A008284(n,m), the number of m parts partitions of n, and e(n,m,q,j) is the exponent of j in the q-th m part partition of n. S2(5;j,1)= A007696(j) = A049029(j,1) = (4*j-3)(!^4), (quadrupel- or 4-factorials).
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EXAMPLE
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[1]; [5,1]; [45,5,1]; [585,70,5,1]; [9945,810,70,5,1];...
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CROSSREFS
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Cf. A134276 (row sums). A134277 (alternating row sums).
Cf. A134151 (S2(4)').
Sequence in context: A000321 A039922 A134274 this_sequence A114154 A134273 A048897
Adjacent sequences: A134272 A134273 A134274 this_sequence A134276 A134277 A134278
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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.uni-karlsruhe.de) Nov 13 2007
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