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A027466
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Triangle whose (i,j)-th entry is binomial(i,j)*7^(i-j).
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6
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1, 7, 1, 49, 14, 1, 343, 147, 21, 1, 2401, 1372, 294, 28, 1, 16807, 12005, 3430, 490, 35, 1, 117649, 100842, 36015, 6860, 735, 42, 1, 823543, 823543, 352947, 84035, 12005, 1029, 49, 1, 5764801, 6588344, 3294172, 941192, 168070, 19208
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| T(i,j) is the number of i-permutations of 8 objects a,b,c,d,e,f,g,h, with repetition allowed, containing j a's. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 21 2007
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REFERENCES
| B. N. Cyvin et al., Isomer enumeration of unbranched catacondensed polygonal systems with pentagons and heptagons, Match, No. 34 (Oct 1996), pp. 109-121.
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FORMULA
| Cube of lower triangular normalized Binomial matrix.
Numerators of lower triangle of (a[ i, j ])^3 where a[ i, j ] = Binomial(i-1, j-1)/2^(i-1) if j<=i, 0 if j>i
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EXAMPLE
| 1
7, 1
49, 14, 1
343, 147, 21, 1
2401, 1372, 294, 28, 1
16807, 12005, 3430, 490, 35, 1
117649, 100842, 36015, 6860, 735, 42, 1
823543, 823543, 352947, 84035, 12005, 1029, 49, 1
5764801, 6588344, 3294172, 941192, 168070, 19208, 1372, 56, 1
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MAPLE
| for i from 0 to 8 do seq(binomial(i, j)*7^(i-j), j = 0 .. i) od; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 21 2007
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CROSSREFS
| Cf. A007318.
Sequence in context: A051931 A188728 A038267 * A075502 A052104 A144450
Adjacent sequences: A027463 A027464 A027465 * A027467 A027468 A027469
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KEYWORD
| nonn,tabl,easy
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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EXTENSIONS
| Simpler definition from N. J. A. Sloane (njas(AT)research.att.com).
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