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# User:Juan M. Marquez

- math lecturer at Dept of Maths, CUCEI, Universidad de Guadalajara, Mex, with two M.Sc. applied and pures maths. Ph.D. candidate CIMAT A.C.

## A two sums of reciprocal problems connected

- has the generating function

## the trick

- multiplied by gives but differentiating implies

- , and simplifying throw us this allows to infer the connection of two G.f's:

The function
is known since Sprugnoli 2006 in his SUMS OF RECIPROCALS OF THE CENTRAL BINOMIAL COEFFICIENTS and
was nowhere...

## follow

- webpage: Sum of reciprocals of
**juanmarqz.wordpress.com**

# NEWS

A164001 counts the number of words ordered by word length on the free product group

Z2*Z3 =<( a, b :|: a^2, b^3 )>

0 -> e, (1)

1 -> a, b (2)

2 -> ab, ba, bb (3)

3 -> aba, abb, bab, bba (4)

4 -> abab, abba, baba, babb, bbab (5)

5 -> ababa, abbab, babab, babba, bbaba, bbabb (7)

6 -> ababab, abbaba, abbabb, bababa, bababb, babbab, bbabab, bbabba (9)

# My TwoCents

at https://oeis.org/A171503 on, as I called: "Siehler Numbers"

at https://oeis.org/A121839 on the sum of reciprocal Catalan Numberrrs

at https://oeis.org/A137243 how many pair of coprimes

at https://oeis.org/A000127 on counting regions