Search: id:A080956
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%I A080956
%S A080956 1,1,0,2,5,9,14,20,27,35,44,54,65,77,90,104,119,135,152,170,189,209,230,
%T A080956 252,275,299,324,350,377,405,434,464,495,527,560,594,629,665,702,740,
%U A080956 779,819,860,902,945,989,1034,1080,1127,1175,1224,1274,1325,1377,1430
%V A080956 1,1,0,-2,-5,-9,-14,-20,-27,-35,-44,-54,-65,-77,-90,-104,-119,-135,-152,
               -170,-189,-209,
%W A080956 -230,-252,-275,-299,-324,-350,-377,-405,-434,-464,-495,-527,-560,-594,
               -629,-665,-702,
%X A080956 -740,-779,-819,-860,-902,-945,-989,-1034,-1080,-1127,-1175,-1224,-1274,
               -1325,-1377
%N A080956 (n+1)(2-n)/2.
%C A080956 Coefficient of x in the polynomial C(n,0)+C(n+1,1)x+C(n+2,2)x(x-1)/2.
%C A080956 Equals A154990 * [1,2,3,...]. [From Gary W. Adamson & Mats Granvik (qntmpkt(AT)yahoo.com), 
               Jan 19 2009]
%F A080956 a(n) = 2(C(n+1, 1)-C(n+2, 2)) = (n+1)(2-n)/2
%F A080956 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]
%F A080956 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]
%F A080956 G.f.: (1-2*x)/(1-x)^3. [R. J. Mathar, (mathar(AT)strw.leidenuniv.nl), 
               Jun 11 2009]
%p A080956 seq(-sum(k-1, k=3..n), n=0..53); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 28 2008
%p A080956 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
%p A080956 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]
%Y A080956 Cf. A000096.
%Y A080956 A154990 [From Gary W. Adamson & Mats Granvik (qntmpkt(AT)yahoo.com), 
               Jan 19 2009]
%Y A080956 Sequence in context: A132315 A132336 A000096 this_sequence A132337 A134189 
               A109470
%Y A080956 Adjacent sequences: A080953 A080954 A080955 this_sequence A080957 A080958 
               A080959
%K A080956 easy,sign
%O A080956 0,4
%A A080956 Paul Barry (pbarry(AT)wit.ie), Mar 01 2003
%E A080956 Adapted Lajos e.g.f. to offset zero R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Jun 11 2009

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