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Search: id:A147998
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| A147998 |
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Numerators of second column of array b(i,j)=(1/j!)*integral (from -i-1 to 1) u(u+1)..(u+j-1) du. a(n)=-n(n+2)=1,-A005563(Lyman). |
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+0
5
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| 0, 1, 0, -3, -8, -15, -24, -35, -48, -63, -80, -99, -120, -143, -168, -195, -224, -255, -288, -323, -360, -399, -440, -483, -528, -575, -624, -675, -728, -783, -840, -899, -960, -1023, -1088, -1155, -1224, -1295, -1368, -1443, -1520, -1599, -1680, -1763
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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From reference,pp.54-56. (Partial) array (i from -1,j from 0): 1,1/2,5/12,9/24,251/720,475/1440; 2,0,4/12,8/24,232/720,448/1440; 3,-3/2,9/12,9/24,243/720,459/1440; 4,-8/2,32/12,0,224/720,448/1440; 5,-15/2,85/12,-55/24,475/720,475/1440; 6,-24/2,180/12,-216/24,2376/720,0. Vertical denominators are 1,2,12,24,=A091137.Vertical numerators k-th differences are (from A091137) A000012,-A007395,A010851,-A010863. Later comments.
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REFERENCES
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P. Curtz Integration numerique des systemes differentiels a conditions initiales Centre de Calcul Scientifique de l'Armement,Arcueil,1969.Now in 35170 Bruz,France.
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FORMULA
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a(n)=-n^2+1, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 27 2008]
G.f.: x*(1-3*x)/(1-x)^3 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Aug 30 2009]
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MATHEMATICA
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a=-3; lst={}; k=3; Do[a+=k; AppendTo[lst, a]; k-=2, {n, 1, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 01 2009]
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CROSSREFS
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Sequence in context: A013648 A005563 A132411 this_sequence A164003 A067998 A060615
Adjacent sequences: A147995 A147996 A147997 this_sequence A147999 A148000 A148001
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KEYWORD
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sign
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), Nov 19 2008
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EXTENSIONS
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More terms, Mathematica. - Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 01 2009
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