A284862 Numerators of exponential expansion of (3/(2*log(1+x)))*(1 - 1/(1+x)^(2/3)).

1, -1, 13, -32, 1666, -13426, 515194, -1432000, 1447711256, -4097653768, 256749458824, -2204786032640, 11533922227138736, -33268276510233104, 577462439822785168, -1674851096410984448, 6621155504764033947008, -34711497070334170000000

Offset

0,3

Comments

This is one half of the numerator of the z-sequence of the Sheffer triangle S2[3,2] given in A225466. See the W. Lang link of A006232 for a- and z- sequences for Sheffer triangles and for references.

The denominators are given in A284863.

The nontrivial recurrence for the column m=0 entries A225466(n, 0) = 2^n from the z-sequence z(n) = 2*a(n)/A284863(n) is: T(n,0) = n*Sum_{k=0..n-1} z(k)*A225466(n-1,k), n >= 1, T(0, 0) = 1.

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = numerator(r(n)), with the rationals (in lowest terms) r(n) = [x^n/n!] (3/(2*log(1+x)))*(1 - 1/(1+x)^(2/3)).

Example

The rationals r(n) begin: 1, -1/3, 13/27, -32/27, 1666/405, -13426/729, 515194/5103, -1432000/2187, 1447711256/295245, -4097653768/98415, 256749458824/649539, ...
The z-sequence is {2*r(n)}, n >= 0.
The nontrivial recurrence for A225466(4, 0) = 16 from this z-sequence is: 16 =  8*(1*8 + (-1/3)*117 + (13/27)*135 + (-32/27)*27).

Crossrefs

Cf. A006232, A225466, A284863.

Sequence in context: A140678 A282721 A206345 * A213686 A050659 A123161

Adjacent sequences: A284859 A284860 A284861 * A284863 A284864 A284865

Keyword

sign,easy

Author

Wolfdieter Lang, Apr 09 2017

Status

approved