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Congruences for the Fishburn Numbers

, 2014
The Fishburn numbers, $\xi(n),$ are defined by a formal power series expansion $$ \sum_{n=0}^\infty \xi(n)q^n = 1 + \sum_{n=1}^\infty \prod_{j=1}^n (1-(1-q)^j). $$ For half of the primes $p$, there is a non--empty set of numbers $T(p)$ lying in $[0,p-1]$
Andrews, George E., Sellers, James A.
core  

The Cause of Lead Poisoning in the Tinning of Metals. [PDF]

J Hyg (Lond), 1908
Duckering GE.
europepmc   +1 more source

Explaining unforeseen congruence relationships between PEND and POND partitions via an Atkin-Lehner involution. [PDF]

Ramanujan J
Sellers JA, Smoot NA.
europepmc   +1 more source

Computer-assisted construction of Ramanujan-Sato series for 1 over π. [PDF]

Ramanujan J
Hemmecke R, Paule P, Radu CS.
europepmc   +1 more source

An extensive analysis of the parity of broken 3-diamond partitions.

J Number Theory, 2013
Radu S, Sellers JA.
europepmc   +1 more source

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Dazhao Tang
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The powers of two as sums over partitions

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Arithmetic properties of ℓ-regular partitions

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Nancy S S Gu
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The partition function in arithmetic progressions

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