A302191 - OEIS

A302191

Numerators of Hurwitz inverse of primes [2,3,5,7,...].

1, -3, 1, -5, -7, 97, -403, 3795, 1683, -67403, 141662, -5744835, -710829, 124489961, -7187558877, 247099181979, -43618981401, -2710990422171, 16455095049450, -1725616801459565, 2828334020055989, 58332444583336295, -2708485501761494555

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

In the ring of Hurwitz sequences all members have offset 0.

REFERENCES

Xing Gao and William F. Keigher, Interlacing of Hurwitz series, Communications in Algebra, 45:5 (2017), 2163-2185, DOI: 10.1080/00927872.2016.1226885

LINKS

Table of n, a(n) for n=0..22.

N. J. A. Sloane, Maple programs for operations on Hurwitz sequences

FORMULA

E.g.f. for A302191/A302192 is 1 / Sum_{n >= 0} prime(n+1)*x^n/n!.

EXAMPLE

1/2, -3/4, 1, -5/8, -7/2, 97/4, -403/4, 3795/16, 1683/2, -67403/4, 141662, -5744835/8, -710829/2, 124489961/2, -7187558877/8, ...

MAPLE

# first load Maple commands for Hurwitz operations from link

s:=[seq(ithprime(n), n=1..64)];

Hinv(s);

CROSSREFS

Cf. A302192, A302193.

Sequence in context: A136437 A137328 A140991 * A261712 A038738 A210741

Adjacent sequences: A302188 A302189 A302190 * A302192 A302193 A302194

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane and William F. Keigher, Apr 12 2018

STATUS

approved