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A024395
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a(n) = n-th elementary symmetric function of the first n+1 positive integers congruent to 2 mod 3.
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2
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1, 7, 66, 806, 12164, 219108, 4591600, 109795600, 2951028000, 88084714400, 2891353030400, 103521905491200, 4015191638617600, 167714507921497600, 7506196028811110400, 358368551285791692800, 18180562447078051328000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| E.g.f.: -(1/3)*ln(1-3*x)/(1-3*x)^(2/3). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 26 2003
For n>=1, a(n-1)=3^(n-1)*n!*sum((-1)^k*binomial(2/3,k)/(n-k),k=0..n-1); [From Milan R. Janjic (agnus(AT)blic.net), Dec 14 2008]
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MATHEMATICA
| Table[ (-1)^(n+1)*Sum[(-3)^(n - k) k (-1)^(n - k) StirlingS1[n+1, k + 1], {k, 0, n}], {n, 1, 30}]
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CROSSREFS
| Cf. A024216.
Sequence in context: A065097 A122705 A185181 * A003286 A197744 A052351
Adjacent sequences: A024392 A024393 A024394 * A024396 A024397 A024398
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| Formula (see Mathematica line), correction and more terms from Victor Adamchik (adamchik(AT)cs.cmu.edu), Jul 21, 2001
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