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User:Juan M. Marquez

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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...


webpage: Sum of reciprocals of


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 on, as I called: "Siehler Numbers"

at on the sum of reciprocal Catalan Numberrrs

at how many pair of coprimes

at on counting regions