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A084633
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Inverse binomial transform of repeated odd numbers.
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6
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1, 0, 2, -4, 8, -16, 32, -64, 128, -256, 512, -1024, 2048, -4096, 8192, -16384, 32768, -65536, 131072, -262144, 524288, -1048576, 2097152, -4194304, 8388608, -16777216, 33554432, -67108864, 134217728, -268435456, 536870912, -1073741824, 2147483648, -4294967296
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = (0^n + (-2)^n)/2, for n > 1, with a(1) = 0.
a(n) = (-1)^n * 2^(n-1) for n > 1.
a(n) = -2*a(n-1) for n > 2.
G.f.: (1 +2*x +2*x^2) / (1+2*x). (End)
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MATHEMATICA
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PROG
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(Magma) [n le 1 select 1-n else (0^n + (-2)^n)/2: n in [0..40]]; //G. C. Greubel,Mar 18 2023
(SageMath) [(0^n + (-2)^n)/2 + int(n==1) for n in range(41)] #G. C. Greubel,Mar 18 2023
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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