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Search: id:A113267
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| A113267 |
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Partial sums of Catalan numbers A000108 multiplied by powers of -8. |
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+0
2
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| 1, -7, 121, -2439, 54905, -1321351, 33281657, -866396551, 23125022329, -629441571207, 17405126104697, -487562768820615, 13806913025988217, -394606681111406983, 11367704830045574777, -329739328993506896263, 9622560010799553435257
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Ninth column (m=8) of triangle A112707 (partial sums of Catalan numbers multiplied by powers of nonpositive numbers).
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FORMULA
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a(n)= A112707(n+8, 8), n>=0.
G.f.: c(-8*x)/(1-x), where c(x):=(1-sqrt(1-4*x))/(2*x) is the o.g.f. of Catalan numbers A000108.
G.f. for unsigned sequence: c(8*x)/(1+x), hence |a(n)| is the convolution of the sequences {C(n)*8^n} and {(-1)^n}, where C(n):=A000108(n).
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CROSSREFS
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Cf. A113266 (m=7).
Sequence in context: A007751 A156955 A095752 this_sequence A012028 A094088 A012043
Adjacent sequences: A113264 A113265 A113266 this_sequence A113268 A113269 A113270
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KEYWORD
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sign,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 31 2005
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