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A125091
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Triangle read by rows: T(n,k)=(1/6)k(k+1)(k+2)binom(n,k) (1<=k<=n).
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0
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1, 2, 4, 3, 12, 10, 4, 24, 40, 20, 5, 40, 100, 100, 35, 6, 60, 200, 300, 210, 56, 7, 84, 350, 700, 735, 392, 84, 8, 112, 560, 1400, 1960, 1568, 672, 120, 9, 144, 840, 2520, 4410, 4704, 3024, 1080, 165, 10, 180, 1200, 4200, 8820, 11760, 10080, 5400, 1650, 220, 11
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| T(n,n)=n(n+1)(n+2)/6 = A000292(n). Sum(T(n,k),k=1..n)=2^n*n(n+2)(n+7)/48 = A055585(n-1).
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EXAMPLE
| Triangle starts:
1;
2, 4;
3, 12, 10;
4, 24, 40, 20;
5, 40, 100, 100, 35;
6, 60, 200, 300, 210, 56;
7, 84, 350, 700, 735, 392, 84;
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MAPLE
| T:=(n, k)->k*(k+1)*(k+2)*binomial(n, k)/6: for n from 1 to 11 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form
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CROSSREFS
| Cf. A055585.
Cf. A000292.
Sequence in context: A143986 A059662 A114883 * A181327 A091861 A200715
Adjacent sequences: A125088 A125089 A125090 * A125092 A125093 A125094
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 19 2006
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 04 2006
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