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Search: id:A081114
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| A081114 |
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Triangle read by rows of T(n,k)=n*T(n-1,k)+n-k starting at T(n,n)=0. |
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+0
1
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| 0, 1, 0, 4, 1, 0, 15, 5, 1, 0, 64, 23, 6, 1, 0, 325, 119, 33, 7, 1, 0, 1956, 719, 202, 45, 8, 1, 0, 13699, 5039, 1419, 319, 59, 9, 1, 0, 109600, 40319, 11358, 2557, 476, 75, 10, 1, 0, 986409, 362879, 102229, 23019, 4289, 679, 93, 11, 1, 0, 9864100, 3628799, 1022298
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Taking the triangle into negative values of n and k would produce results close to (k+1)*e*n! - 1, i.e. one less than multiples of A000522 for nonnegative n.
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FORMULA
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For k>0, T(n, k)=ceiling[ (A001339(k-1)/(k-1)! - (k-1)*e) *n! - 1] where A001339(k-1)=ceiling[(k-1)!*(k-1)*e for k>1]. T(n, 0)=floor[e*n! - 1] for n>0; T(n, 1)=n!-1. T(n, n)=0; T(n, n-1)=n+2; T(n, n-2)=n^2+3n+5=A027688(n+1).
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EXAMPLE
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Rows start: 0; 1,0; 4,1,0; 15,5,1,0; 64,23,6,1,0; 325,119,33,7,1,0; etc.
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CROSSREFS
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Columns include A007526 and A033312.
Sequence in context: A048516 A060638 A007789 this_sequence A069018 A130636 A117414
Adjacent sequences: A081111 A081112 A081113 this_sequence A081115 A081116 A081117
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KEYWORD
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nonn,tabl
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Apr 16 2003
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