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A079901
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Triangle of powers, T(n,k) = n^k, 0<=k<=n, read by rows.
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11
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1, 1, 1, 1, 2, 4, 1, 3, 9, 27, 1, 4, 16, 64, 256, 1, 5, 25, 125, 625, 3125, 1, 6, 36, 216, 1296, 7776, 46656, 1, 7, 49, 343, 2401, 16807, 117649, 823543, 1, 8, 64, 512, 4096, 32768, 262144, 2097152, 16777216, 1, 9, 81, 729, 6561, 59049, 531441, 4782969, 43046721
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| T(n,k) = if k=0 then 1 else T(n,k-1)*n;
T(n,0)=1; T(n,1)=n for n>0; T(n,2)=A000290(n) for n>1; T(n,3)=A000578(n) for n>2; T(n,4)=A000583(n) for n>3;
T(n,n-2)=A000272(n) for n>2; T(n,n-1)=A000169(n) for n>1; T(n,n)=A000312(n).
Matrix inverse equals the triangle R where R(n,k) = A107045(n,k)/A107046(n,k) are coefficients with exponential-like properties. - Paul D. Hanna (pauldhanna(AT)juno.com), May 22 2005
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CROSSREFS
| Cf. A107045/A107046 (matrix inverse).
Sequence in context: A100075 A059836 A069270 * A121426 A190183 A004515
Adjacent sequences: A079898 A079899 A079900 * A079902 A079903 A079904
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KEYWORD
| nonn,tabl
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 21 2003
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