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A111377
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Triangle of sum of product of partitions of n where largest part is k.
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0
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1, 1, 2, 1, 2, 3, 1, 6, 3, 4, 1, 6, 9, 4, 5, 1, 14, 18, 12, 5, 6, 1, 14, 30, 24, 15, 6, 7, 1, 30, 48, 56, 30, 18, 7, 8, 1, 30, 99, 80, 70, 36, 21, 8, 9, 1, 62, 135, 180, 125, 84, 42, 24, 9, 10, 1, 62, 237, 276, 250, 150, 98, 48, 27, 10, 11, 1, 126, 390, 540, 420, 336, 175, 112, 54, 30
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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FORMULA
| T(n, k)=k*sum_j {0<=j<=k} a(n-k, j) starting with T(0, 0)=1; T(n, n)=n for n>=1.
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EXAMPLE
| Triangle starts 1; 1,2; 1,2,3; 1,6,3,4; 1,6,9,4,5; 1,14,18,12,5,6; etc.
T(6,3)=18 since partitions of 6 with largest part 3 is 3+3, 3+2+1, 3+1+1+1 and 3*3 + 3*2*1 + 3*1*1*1 = 18.
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CROSSREFS
| Row sums are A006906.
Sequence in context: A078032 A162453 A008313 * A014046 A128065 A018194
Adjacent sequences: A111374 A111375 A111376 * A111378 A111379 A111380
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KEYWORD
| nonn,tabl
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Nov 09 2005
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