A284857 Numerators of the exponential expansion of (3/(log(1+x)))*(1 - 1/(1+x)^(1/3)).

1, -1, 11, -49, 1187, -18083, 662407, -3539605, 864309187, -949103125, 289289620393, -4846044126449, 12389144856368069, -69977996793541583, 1191089380720588487, -6783915816877925461, 3295296805315071712171, -169986671194174827887881, 129921413307474873885175559, -149671376459098924087260625

Offset: 0

Author

Wolfdieter Lang, Apr 04 2017

Keywords

• sign
• easy

Comments

For the denominators see A284858.

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.

Examples

			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)).
		

Crossrefs

Cf. A284858 (denominators), A282629, A006232/A006233.

Formula

E.g.f.: (3/(log(1+x)))*(1 - 1/(1+x)^(1/3)) for the rational sequence a(n)/A284858(n), n >= 0.