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A134400
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M * A007318, where M = triangle with (1, 1, 2, 3,...) in the main diagonal and the rest zeros.
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4
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1, 1, 1, 2, 4, 2, 3, 9, 9, 3, 4, 16, 24, 16, 4, 5, 25, 50, 50, 25, 5, 6, 36, 90, 120, 90, 36, 6, 7, 49, 147, 245, 245, 147, 49, 7, 8, 64, 224, 448, 560, 448, 224, 64, 8, 9, 81, 324, 756, 1134, 1134, 756, 324, 81, 9
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Row sums = A134401: (1, 2, 8, 24, 64, 160, 384,...).
Triangle T(n,k), read by rows, given by [1,1,-1,1,0,0,0,0,0,...] DELTA [1,1,-1,1,0,0,0,0,0,...] where DELTA is the operator defined in A084938 . A134402*A007318 as infinite lower triangular matrices . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 26 2007
From n athletes, select a team of k players and then choose a coach who is allowed to be on the team or not. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Mar 13 2010]
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FORMULA
| T(n,k) = n * Binomial(n,k) E.g.f. for column k is: (x^k/k!)exp(x)(x+k) [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Mar 13 2010]
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EXAMPLE
| First few rows of the triangle are:
1;
1, 1;
2, 4, 2;
3, 9, 9, 3;
4, 16, 24, 16, 4;
5, 25, 50, 50, 25, 5;
6, 36, 90, 120, 90, 36, 6;
7, 49, 147, 245, 245, 147, 49, 7;
...
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MAPLE
| with(combstruct):for n from 0 to 10 do seq(n*count(Combination(n), size=m), m = 0 .. n) od; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 09 2008
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MATHEMATICA
| Table[Table[n*Binomial[n, k], {k, 0, n}], {n, 0, 10}] // Grid [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Mar 13 2010]
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CROSSREFS
| Cf. A134401.
A134400(n,k) = A003506(n,k) + A003506(n,k-1) [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Mar 13 2010]
Sequence in context: A093056 A151849 A141387 * A016095 A181399 A165464
Adjacent sequences: A134397 A134398 A134399 * A134401 A134402 A134403
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 23 2007
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