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%I #20 Nov 01 2017 15:20:50
%S 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,
%T 2,13,64,147,155,61,4,12,54,112,105,36,2,15,89,264,406,301,85,4,14,77,
%U 210,294,196,49,2,17,118,429,870,966,532,113,4,16,104,352,660,672,336,64,2
%N Irregular triangle read by rows: numbers b_m(i) related to Bernoulli and Euler polynomials.
%C See the Sun (2008) reference for the (complicated) precise definition.
%C It appears that every second row equals every second row of A034807. - _Ralf Stephan_, Oct 26 2013
%H Zhi-Wei Sun, <a href="https://arxiv.org/abs/math/0404385">On sums of binomial coefficients and their applications</a>, arXiv:math/0404385 [math.NT], 2004-2008.
%H Zhi-Wei Sun, <a href="https://doi.org/10.1016/j.disc.2007.08.046">On sums of binomial coefficients and their applications</a>, Discrete Math. 308 (2008), no. 18, 4231--4245. MR2427754(2010d:05002).
%e Triangle begins:
%e 2
%e 5 4
%e 4 2
%e 7 13 4
%e 6 9 2
%e 9 26 25 4
%e 8 20 16 2
%e 11 43 70 41 4
%e 10 35 50 25 2
%e 13 64 147 155 61 4
%e 12 54 112 105 36 2
%e ...
%o (PARI)
%o c(m,i) = binomial(m+1-i,i)*(m*m+m-2*i)/((m-i)*(m+1-i));
%o d(m,i) = binomial(m-i,i)*m/(m-i);
%o b(m,i) = if ( m%2==0, d(m,i), c(m,i) );
%o for (m=2,16, for (i=1,ceil(m/2), print1( b(m,i), ", " ))) \\ _Hugo Pfoertner_, Nov 01 2017
%Y Cf. A034807, A211246, A267633.
%K nonn,tabf
%O 2,1
%A _N. J. A. Sloane_, Apr 05 2012
%E Corrected and extended by _Hugo Pfoertner_, Nov 01 2017
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