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Search: id:A112710
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| A112710 |
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Partial sums of Catalan numbers A000108 multiplied by powers of -3. |
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+0
3
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| 1, -2, 16, -119, 1015, -9191, 87037, -851186, 8531044, -87167702, 904619302, -9509144240, 101036961052, -1083385595648, 11708378016712, -127402051267703, 1394629704432367, -15347719608268403, 169699299111055897, -1884322608673443833, 21003350078068124587
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Fourth column (m=3) 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+3, 3), n>=0.
G.f.: c(-3*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(3*x)/(1+x), hence |a(n)| is the convolution of the sequences {C(n)*3^n} and {(-1)^n}, where C(n):=A000108(n).
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CROSSREFS
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Cf. A064306 (unsigned m=2 case).
Sequence in context: A159324 A088755 A136782 this_sequence A046105 A086854 A026129
Adjacent sequences: A112707 A112708 A112709 this_sequence A112711 A112712 A112713
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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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