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Search: id:A080956
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| 1, 1, 0, -2, -5, -9, -14, -20, -27, -35, -44, -54, -65, -77, -90, -104, -119, -135, -152, -170, -189, -209, -230, -252, -275, -299, -324, -350, -377, -405, -434, -464, -495, -527, -560, -594, -629, -665, -702, -740, -779, -819, -860, -902, -945, -989, -1034, -1080, -1127, -1175, -1224, -1274, -1325, -1377
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Coefficient of x in the polynomial C(n,0)+C(n+1,1)x+C(n+2,2)x(x-1)/2.
Equals A154990 * [1,2,3,...]. [From Gary W. Adamson & Mats Granvik (qntmpkt(AT)yahoo.com), Jan 19 2009]
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FORMULA
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a(n) = 2(C(n+1, 1)-C(n+2, 2)) = (n+1)(2-n)/2
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,n-1,2), for n>=3. [From Milan R. Janjic (agnus(AT)blic.net), Dec 20 2008]
E.g.f.: exp(x)*(1-x^2/2) . [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 05 2009, R. J. Mathar, Jun 11 2009]
G.f.: (1-2*x)/(1-x)^3. [R. J. Mathar, (mathar(AT)strw.leidenuniv.nl), Jun 11 2009]
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MAPLE
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seq(-sum(k-1, k=3..n), n=0..53); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 28 2008
a[0]:=0:a[1]:=1:for n from 2 to 54 do a[n]:=2*a[n-1]-a[n-2]-1 od: seq(a[n], n=1..54); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 18 2008
restart: G(x):=exp(x)*(x-x^2/2): f[0]:=G(x): for n from 1 to 54 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=1..54 ); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 05 2009]
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CROSSREFS
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Cf. A000096.
A154990 [From Gary W. Adamson & Mats Granvik (qntmpkt(AT)yahoo.com), Jan 19 2009]
Sequence in context: A132315 A132336 A000096 this_sequence A132337 A134189 A109470
Adjacent sequences: A080953 A080954 A080955 this_sequence A080957 A080958 A080959
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KEYWORD
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easy,sign
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Mar 01 2003
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EXTENSIONS
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Adapted Lajos e.g.f. to offset zero R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 11 2009
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