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A084902
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5^(n-1)n(n+1)/2.
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2
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0, 1, 15, 150, 1250, 9375, 65625, 437500, 2812500, 17578125, 107421875, 644531250, 3808593750, 22216796875, 128173828125, 732421875000, 4150390625000, 23345947265625, 130462646484375, 724792480468750, 4005432128906250
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Binomial transform of A084901. Fourth binomial transform of heptagonal numbers A000566. Fifth binomial transform of (0,1,5,0,0,0,....).
Number of n-permutations of 6 objects u, v, w, z, x, y with repetition allowed, containing exactly two u's. Example: a(2)=15 because we have : uuw, uuv, uuz, uux, uuy, uwu, uvu, uzu, uxu, uyu, wuu, vuu, zuu, xuu, yuu - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 30 2007
A shifted version of A081135. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 17 2008]
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FORMULA
| G.f.: x/(1 - 5x)^3
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MAPLE
| seq(seq(binomial(i+1, j)*5^(i-1), j =i-1), i=0..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 30 2007
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PROG
| (Other) SAGE:[lucas_number2(n, 5, 0)*binomial(n, 2)/5^2 for n in xrange(1, 22)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 12 2009]
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CROSSREFS
| Cf. A038243.
Sequence in context: A022739 A085375 A081135 * A021364 A206366 A016103
Adjacent sequences: A084899 A084900 A084901 * A084903 A084904 A084905
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jun 10 2003
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