OFFSET
0,2
COMMENTS
REFERENCES
Umberto Scarpis, Sui numeri primi e sui problemi dell'analisi indeterminata in Questioni riguardanti le matematiche elementari, Nicola Zanichelli Editore (1924-1927, third edition), page 11.
J. V. Uspensky and M. A. Heaslet, Elementary Number Theory, McGraw-Hill, NY, 1939, p. 103.
LINKS
Alexander Borisov, Quotient singularities, integer ratios of factorials and the Riemann Hypothesis, arXiv:math/0505167 [math.NT], 2005; International Mathematics Research Notices, Vol. 2008, Article ID rnn052, page 2 (Theorem 2).
Ira Gessel, Integer quotients of factorials and algebraic multivariable hypergeometric series, MIT Combinatorics Seminar, September 2011 (slides).
Hans-Christian Herbig and Mateus de Jesus Gonçalves, On the numerology of trigonometric polynomials, arXiv:2311.13604 [math.HO], 2023.
Kevin Limanta and Norman Wildberger, Super Catalan Numbers, Chromogeometry, and Fourier Summation over Finite Fields, arXiv:2108.10191 [math.CO], 2021. See Table 1 p. 2 where terms are shown as an array.
EXAMPLE
Triangle begins:
1;
2, 2;
6, 4, 6;
20, 10, 12, 20;
70, 28, 28, 40, 70;
252, 84, 72, 90, 140, 252;
924, 264, 198, 220, 308, 504, 924;
3432, 858, 572, 572, 728, 1092, 1848, 3432;
12870, 2860, 1716, 1560, 1820, 2520, 3960, 6864, 12870;
48620, 9724, 5304, 4420, 4760, 6120, 8976, 14586, 25740, 48620;
...
MATHEMATICA
Flatten[Table[Table[(2 k)! ((2 n)!/(k! n! (k + n)!)), {k, 0, n}], {n, 0, 9}]]
PROG
(Magma)
[Factorial(2*k)*Factorial(2*n)/(Factorial(k)*Factorial(n)*Factorial(k+n)): k in [0..n], n in [0..9]];
CROSSREFS
AUTHOR
Bruno Berselli, Apr 27 2012
STATUS
approved