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A067417
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Triangle with columns built from certain power sequences.
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9
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1, 3, 1, 9, 4, 1, 27, 24, 5, 1, 81, 144, 45, 6, 1, 243, 864, 405, 72, 7, 1, 729, 5184, 3645, 864, 105, 8, 1, 2187, 31104, 32805, 10368, 1575, 144, 9, 1, 6561, 186624, 295245, 124416, 23625, 2592, 189, 10, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The column sequences (without leading 0's) give: A000244 (powers of 3), A067411 for m=0..1 and A067419-24 for m=3..8. The third column (m=2) is A067403.
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FORMULA
| a(n, m)= 1 if n=m; a(n, m)= (m+3)*(3*(m+1))^(n-m-1) if n>m>=0, else 0.
G.f. for column m: (x^m)*(1-2*m*x)/(1-3*(m+1)*x).
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EXAMPLE
| {1}; {3,1}; {9,4,1}; {27,24,5,1}; ...
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CROSSREFS
| Cf. A009998 (triangle built from powers of (m+1)), A067402, A067410.
Sequence in context: A054448 A106516 A140071 * A187887 A016577 A124573
Adjacent sequences: A067414 A067415 A067416 * A067418 A067419 A067420
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KEYWORD
| nonn,easy,tabl
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jan 25 2002
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