OFFSET
1,5
COMMENTS
Convolution triangle of Narayana's cows sequence A000930. - Peter Luschny, Oct 09 2022
FORMULA
T(n,m)=sum(k=0..n-m, binomial(k,(n-m-k)/2)*binomial(m+k-1,m-1)*((-1)^(n-m-k)+1))/2.
EXAMPLE
Triangle T(n, m) starts:
[1] 1;
[2] 1, 1;
[3] 1, 2, 1;
[4] 2, 3, 3, 1;
[5] 3, 6, 6, 4, 1;
[6] 4, 11, 13, 10, 5, 1;
[7] 6, 18, 27, 24, 15, 6, 1;
[8] 9, 30, 51, 55, 40, 21, 7, 1;
[9] 13, 50, 94, 116, 100, 62, 28, 8, 1;
.
From R. J. Mathar, Mar 15 2013: (Start)
The matrix inverse starts
1;
-1,1;
1,-2,1;
-2,3,-3,1;
5,-6,6,-4,1;
-11,15,-13,10,-5,1;
24,-36,33,-24,15,-6,1;
-57,84,-84,63,-40,21,-7,1;
141,-204,208,-168,110,-62,28,-8,1.
(End)
MAPLE
A202191 := proc(n, k)
(x/(1-x-x^3))^k ;
coeftayl(%, x=0, n) ;
end proc: # R. J. Mathar, Mar 15 2013
# Uses function PMatrix from A357368. Adds column 1, 0, 0, ... to the left.
PMatrix(10, n -> simplify(hypergeom([(2 - n)/3, (3 - n)/3, (1 - n)/3], [(2 - n)/2, (1 - n)/2], -27/4))); # Peter Luschny, Oct 09 2022
PROG
(Maxima)
T(n, m):=sum(binomial(k, (n-m-k)/2)*binomial(m+k-1, m-1)*((-1)^(n-m-k)+1), k, 0, n-m)/2;
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Vladimir Kruchinin, Dec 14 2011
STATUS
approved