- 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