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A249996
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Expansion of 1/((1+2*x)*(1+3*x)*(1-4*x)).
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3
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1, -1, 15, -5, 191, 99, 2455, 3515, 33231, 74899, 474695, 1371435, 7071871, 23520899, 108399735, 390617755, 1691480111, 6378762099, 26676785575, 103221406475, 423343881951, 1661998662499, 6742129440215, 26686105001595, 107591675061391, 427824901526099, 1718925069371655
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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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G.f.: 1 / ((1+2*x)*(1+3*x)*(1-4*x)).
a(n) = ( 2^(3+2*n) + (3^(3+n)-7*2^(1+n))*(-1)^n )/21. - Colin Barker, Dec 29 2014
a(n) = -a(n-1) + 14*a(n-2) + 24*a(n-3). - Colin Barker, Dec 29 2014
E.g.f.: (1/21)*(27*exp(-3*x) - 14*exp(-2*x) + 8*exp(4*x)). - G. C. Greubel, Oct 11 2022
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MATHEMATICA
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LinearRecurrence[{-1, 14, 24}, {1, -1, 15}, 41] (* G. C. Greubel, Oct 11 2022 *)
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PROG
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(PARI) Vec(1/((1+2*x)*(1+3*x)*(1-4*x)) + O(x^50)) \\ Michel Marcus, Dec 29 2014
(Magma) [(2^(2*n+3) +(-1)^n*(3^(n+3) -7*2^(n+1)))/21: n in [0..40]]; // G. C. Greubel, Oct 11 2022
(SageMath) [(2^(2*n+3) +(-1)^n*(3^(n+3) -7*2^(n+1)))/21 for n in range(41)] # G. C. Greubel, Oct 11 2022
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CROSSREFS
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Cf. A016269: expansion of 1/((1-2*x)*(1-3*x)*(1-4*x)).
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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