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A285062 Numerators of the exponential expansion of (4/(log(1+x)))*(1-1/(1+x)^(1/4)). 2
1, -1, 7, -81, 3853, -25721, 1862773, -52571875, 2828694491, -20554196553, 2489317910533, -36843139557745, 187344440646279463, -200535626786994961, 15853768141768274581, -319644021424695652161, 927777140067161706072467, -1412565248386878259675625, 2151379749437782936765977859 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This gives the numerators of the z-sequence for the Sheffer triangle (exp(x), exp(4*x) - 1) shown in A285061. 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 4*A006232/A006233.

For the nontrivial recurrence for the sequence {1^n} of column m=0 of A285061 by the z-sequence see the example n=4 below.

LINKS

Table of n, a(n) for n=0..18.

FORMULA

The e.g.f. of the rationals r(n) = a(n)/A285063(n) is (4/(log(1+x)))*(1 - 1/(1+x)^(1/4)).

EXAMPLE

The rationals r(n) = a(n)/A285063(n),  n >= 0,  start: 1, -1/8, 7/48, -81/256, 3853/3840, -25721/6144, 1862773/86016, -52571875/393216, 2828694491/2949120, -20554196553/2621440, ...

The z-Recurrence for A285061(4, 0) = 1 is  1 = 4*(1*1 + 124*(-1/8) + 240*(7/48) + 64*(-81/256)).

CROSSREFS

Cf. A006232, A006232/A006233, A285061.

Sequence in context: A088735 A112119 A058575 * A253265 A304870 A191804

Adjacent sequences:  A285059 A285060 A285061 * A285063 A285064 A285065

KEYWORD

sign,frac,easy

AUTHOR

Wolfdieter Lang, Apr 13 2017

STATUS

approved

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Last modified September 28 04:37 EDT 2020. Contains 337392 sequences. (Running on oeis4.)