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A067402
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Triangle with columns built from certain power sequences.
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9
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1, 1, 1, 1, 3, 1, 1, 12, 5, 1, 1, 48, 45, 7, 1, 1, 192, 405, 112, 9, 1, 1, 768, 3645, 1792, 225, 11, 1, 1, 3072, 32805, 28672, 5625, 396, 13, 1, 1, 12288, 295245, 458752, 140625, 14256, 637, 15, 1, 1, 49152, 2657205, 7340032, 3515625, 513216, 31213
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| The column sequences (without leading 0's)give: A000012, A002001, A067403-A067409 for m=0..8. The tenth column (m=9) gives [1, 19, 1900, 190000,...].
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FORMULA
| a(n, m)= 1 if n=m; a(n, m)= (2*m+1)*(m+1)^(2*(n-m-1)) if n>m>=0, else 0.
G.f. for column m: (x^m)*(1-x*m^2)/(1-x*(m+1)^2).
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EXAMPLE
| {1}; {1,1}; {1,3,1}; {1,12,5,1}; ...
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CROSSREFS
| Cf. A009998 (triangle built from powers of (m+1)).
Sequence in context: A176421 A168552 A111473 * A113340 A134523 A098778
Adjacent sequences: A067399 A067400 A067401 * A067403 A067404 A067405
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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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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Jun 11 2002
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