proposed

approved

editing

proposed

T(n,k)} = Sum_{j=0..k } binomial(j,((n-k-2*j)/2))*binomial(k,j)*((-1)^(n-k)+1))/2.

approved

editing

editing

approved

end proc:

end proc: seq(seq(A191238(n, m), m=1..n), n=1..10) ; # R. J. Mathar, Dec 16 2015

approved

editing

proposed

approved

editing

proposed

Vladimir Kruchinin and D. V. Kruchinin, <a href="http://arxiv.org/abs/1103.2582">Composita and their properties</a>, arXiv:1103.2582 [math.CO], 2011-2013.

Vladimir Kruchinin, <a href="http://arxiv.org/abs/1104.5065">Derivation of Bell Polynomials of the Second Kind</a>, arXiv:1104.5065 [math.CO], 2011.

Vladimir Kruchinin, <a href="http://arxiv.org/abs/1104.5065">Derivation of Bell Polynomials of the Second Kind</a>, arXiv:1104.5065 [math.CO], 2011.

Vladimir Kruchinin and D. V. Kruchinin, <a href="http://arxiv.org/abs/1103.2582">Composita and their properties</a>, arXiv:1103.2582 [math.CO], 2011-2013.

Vladimir Kruchinin, and D. V. Kruchinin, <a href="http://arxiv.org/abs/1103.2582">Composita and their properties</a>, arXiv:1103.2582 [math.CO], 2011-2013.

Vladimir Kruchinin, <a href="http://arxiv.org/abs/1104.5065">Derivation of Bell Polynomials of the Second Kind</a>, arXiv:1104.5065 [math.CO], 2011.

Milan Janjic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Janjic/janjic73.html">Binomial Coefficients and Enumeration of Restricted Words</a>, Journal of Integer Sequences, 2016, Vol 19, #16.7.3.

T(n,k)} =sum( Sum_{j=0..k, binomial(j,((n-k-2*j)/2))*binomial(k,j)*((-1)^(n-k)+1))/2.

triangle Triangle begins:

1,

0,1,

1,0,1,

0,2,0,1,

1,0,3,0,1,

0,3,0,4,0,1,

0,0,6,0,5,0,1,

0,2,0,10,0,6,0,1,

0,0,7,0,15,0,7,0,1,

0,1,0,16,0,21,0,8,0,1

approved

editing

Milan Janjic, <a href="httphttps://www.emiscs.amsuwaterloo.orgca/journals/JIS/VOL19/Janjic/janjic73.html">Binomial Coefficients and Enumeration of Restricted Words</a>, Journal of Integer Sequences, 2016, Vol 19, #16.7.3