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Search: id:A134146
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| A134146 |
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Triangle of numbers obtained from the partition array A134145. |
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5
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| 1, 3, 1, 15, 3, 1, 105, 24, 3, 1, 945, 150, 24, 3, 1, 10395, 1485, 177, 24, 3, 1, 135135, 14805, 1620, 177, 24, 3, 1, 2027025, 191520, 16425, 1701, 177, 24, 3, 1, 34459425, 2687580, 208125, 16830, 1701, 177, 24, 3, 1, 654729075, 44552025, 2880360, 212985
(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(3)'.
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(3;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(3;j,1)= A001147(j) = A035342(j,1) = (2*j-1)!!.
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EXAMPLE
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[1]; [3,1]; [15,3,1]; [105,24,3,1]; [945,150,24,3,1];...
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CROSSREFS
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Cf. A134147 (row sums).
Cf. A134148 (allternating row sums).
Cf. A134134 (k=2 member of this triangle family).
Sequence in context: A128042 A108083 A134145 this_sequence A085569 A072479 A131440
Adjacent sequences: A134143 A134144 A134145 this_sequence A134147 A134148 A134149
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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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