A302194 Hurwitz inverse of [1 followed by primes], [1,2,3,5,7,...].

1, -2, 5, -17, 79, -471, 3391, -28451, 272447, -2933807, 35102403, -462021525, 6634207777, -103200019093, 1728836723813, -31030630439249, 594094812208133, -12085090282079299, 260296103744105623, -5917885334682695549, 141625618336446419151

Offset: 0

Author

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

Keywords

• sign

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

• Seiichi Manyama, Table of n, a(n) for n = 0..436
• N. J. A. Sloane, Maple programs for operations on Hurwitz sequences

Crossrefs

Cf. A302191, A302192.

Programs

Maple

# first load Maple commands for Hurwitz operations from link
s:=[1, seq(ithprime(n),n=1..64)];
Hinv(s);

Formula

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