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Search: id:A067402
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| A067402 |
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Triangle with columns built from certain power sequences. |
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+0
10
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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; listen)
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OFFSET
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0,5
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COMMENT
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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
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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
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{1}; {1,1}; {1,3,1}; {1,12,5,1}; ...
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CROSSREFS
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Cf. A009998 (triangle built from powers of (m+1)).
Sequence in context: A103997 A013561 A111473 this_sequence A113340 A134523 A098778
Adjacent sequences: A067399 A067400 A067401 this_sequence A067403 A067404 A067405
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jan 25 2002
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Jun 11 2002
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