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Search: id:A112711
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| A112711 |
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Partial sums of Catalan numbers A000108 multiplied by powers of -4. |
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+0
3
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| 1, -3, 29, -291, 3293, -39715, 500957, -6527779, 87188701, -1187355427, 16424527069, -230141827875, 3259720426717, -46595454638883, 671319066305757, -9738441487391523, 142121594825368797, -2085158937761782563, 30737922595101500637, -455043684091275090723
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Fifth column (m=4) 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+4, 4), n>=0.
G.f.: c(-4*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(4*x)/(1+x), hence |a(n)| is the convolution of the sequences {C(n)*4^n} and {(-1)^n}, where C(n):=A000108(n).
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CROSSREFS
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Cf. A112710 (m=3).
Sequence in context: A025186 A140780 A002669 this_sequence A001947 A049038 A091646
Adjacent sequences: A112708 A112709 A112710 this_sequence A112712 A112713 A112714
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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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