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A284857
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Numerators of the exponential expansion of (3/(log(1+x)))*(1 - 1/(1+x)^(1/3)).
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3
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1, -1, 11, -49, 1187, -18083, 662407, -3539605, 864309187, -949103125, 289289620393, -4846044126449, 12389144856368069, -69977996793541583, 1191089380720588487, -6783915816877925461, 3295296805315071712171, -169986671194174827887881, 129921413307474873885175559, -149671376459098924087260625
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OFFSET
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0,3
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COMMENTS
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This gives the numerators of the z-sequence for the Sheffer triangle (exp(x), exp(3*x) - 1) shown in A282629. For the notion and use of a- and z- sequences for Sheffer triangles see the W. Lang link under A006232. The a-sequence of this Sheffer triangle is given by A006232/A006233.
For the nontrivial decompositions of 1 given by the z-sequence recurrence for the m=0 column repeat(1) of the triangle A282629 see an example there and below.
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LINKS
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FORMULA
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E.g.f.: (3/(log(1+x)))*(1 - 1/(1+x)^(1/3)) for the rational sequence a(n)/A284858(n), n >= 0.
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EXAMPLE
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The rationals a(n)/A284858(n) start: 1, -1/6, 11/54, -49/108, 1187/810, -18083/2916, 662407/20412, -3539605/17496, 864309187/590490, -949103125/78732, 289289620393/2598156, -4846044126449/4251528, 12389144856368069/967222620, -69977996793541583/446410440, 1191089380720588487/573956280, -6783915816877925461/229582512, ...
From the z-recurrence for A282629(5, 0) = 1 one finds: 1 = 5*(1*1 + 255*(-1/6) + 945*(11/54) + 594*(-49/108) + 81*(1187/810)).
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CROSSREFS
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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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