On sums related to central binomial and trinomial coefficients

Details On sums related to central binomial and trinomial coefficients On sums related to central binomial and trinomial coefficients

2011-01-03

arxiv.org/abs/1101.0600v24

Mathematics

Number Theory

38 pages, submitted version

Scientific paper

A generalized central trinomial coefficient T_n(b,c) is the coefficient of x^n in the expansion of (x^2+bx+c)^n with b and c integers. In this paper we investigate congruences and series for sums of terms related to both central binomial coefficients and generalized central trinomial coefficients. The paper contains many conjectures on congruences and 48 proposed new series for $1/\pi$ motivated by congruences and related dualities.

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