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A211247
Irregular triangle read by rows: numbers b_m(i) related to Bernoulli and Euler polynomials.
1
2, 5, 4, 4, 2, 7, 13, 4, 6, 9, 2, 9, 26, 25, 4, 8, 20, 16, 2, 11, 43, 70, 41, 4, 10, 35, 50, 25, 2, 13, 64, 147, 155, 61, 4, 12, 54, 112, 105, 36, 2, 15, 89, 264, 406, 301, 85, 4, 14, 77, 210, 294, 196, 49, 2, 17, 118, 429, 870, 966, 532, 113, 4, 16, 104, 352, 660, 672, 336, 64, 2
OFFSET
2,1
COMMENTS
See the Sun (2008) reference for the (complicated) precise definition.
It appears that every second row equals every second row of A034807. - Ralf Stephan, Oct 26 2013
LINKS
Zhi-Wei Sun, On sums of binomial coefficients and their applications, arXiv:math/0404385 [math.NT], 2004-2008.
Zhi-Wei Sun, On sums of binomial coefficients and their applications, Discrete Math. 308 (2008), no. 18, 4231--4245. MR2427754(2010d:05002).
EXAMPLE
Triangle begins:
2
5 4
4 2
7 13 4
6 9 2
9 26 25 4
8 20 16 2
11 43 70 41 4
10 35 50 25 2
13 64 147 155 61 4
12 54 112 105 36 2
...
PROG
(PARI)
c(m, i) = binomial(m+1-i, i)*(m*m+m-2*i)/((m-i)*(m+1-i));
d(m, i) = binomial(m-i, i)*m/(m-i);
b(m, i) = if ( m%2==0, d(m, i), c(m, i) );
for (m=2, 16, for (i=1, ceil(m/2), print1( b(m, i), ", " ))) \\ Hugo Pfoertner, Nov 01 2017
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Apr 05 2012
EXTENSIONS
Corrected and extended by Hugo Pfoertner, Nov 01 2017
STATUS
approved