A302199 Hurwitz inverse of partition numbers A000041.

1, -1, 0, 3, -5, -17, 103, 55, -2680, 6720, 82446, -642698, -2087303, 53641331, -96015983, -4454066000, 35131380473, 323923309109, -6776856484915, -3620043398324, 1159030195119059, -7865002945782432, -175052008152354596, 3163635176513031787

Offset: 0

Author

N. J. A. Sloane and William F. Keigher, Apr 14 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..482

Crossrefs

Cf. A000041, A302189.

Programs

Maple

# first load Maple commands for Hurwitz operations from link in A302189.
with(combinat);
s:=[seq(numbpart,n=0..40)];
Hinv(s);

Formula

E.g.f. = 1 / Sum_{n >= 0} partition(n)*x^n/n!.