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1, 3, -1, 0, 4, -28, 188, -1368, 11016, -98208, 964512, -10370880, 121337280, -1535880960, 20924455680, -305396421120, 4755302899200, -78700195123200, 1379748896870400, -25546854999859200, 498194992408780800, -10207190048993280000, 219216795045212160000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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COMMENTS
| If we eliminate the first term and set a(0)=3, then a(0)..a(12) = (-1)^(n+1)*n!*(2*H(n)-3)..where H(n) is the n'th harmonic number [From Gary Detlefs (gdetlefs(AT)aol.com), Feb 13 2010]
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REFERENCES
| L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 139, b(n,2).
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FORMULA
| E.g.f.: ((1+x)*ln(1+x))^2/2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 20 2003
a(n)=sum(i=1, n-1, i^2*Stirling1(n-1, i)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 23 2004
If we define f(n,i,a)=sum(binomial(n,k)*stirling1(n-k,i)*product(-a-j,j=0..k-1),k=0..n-i), then a(n) = f(n,2,-2), for n>=2. [From Milan R. Janjic (agnus(AT)blic.net), Dec 21 2008]
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MAPLE
| with(combinat): for n from 2 to 40 do for k from 2 to 2 do printf(`%d, `, sum(binomial(l, k)*k^(l-k)*stirling1(n, l), l=k..n)) od: od:
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CROSSREFS
| Sequence in context: A117372 A127570 A186827 * A143468 A133728 A127627
Adjacent sequences: A045403 A045404 A045405 * A045407 A045408 A045409
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KEYWORD
| sign,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 26 2001
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jan 26 2001
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