OFFSET
0,6
LINKS
E. Munarini, M. Poneti, and S. Rinaldi, Matrix compositions, JIS 12 (2009) 09.4.8, Table 4.
EXAMPLE
1 ;
0 1 ;
0 1 3 ;
0 3 12 13 ;
0 4 45 108 75;
0 7 148 672 1056 541 ;
0 14 477 3622 10028 11520 4683 ;
0 23 1502 18174 79508 155840 140256 47293;
0 39 4678 87474 570521 1705915 2566554 1894032 545835;
MAPLE
z := proc(n, m)
kmax := n+1 ;
add((-1)^k*(1-(1-x^k)^m)/(1-x^k)^m, k=1..kmax) ;
1/(1+%) ;
coeftayl(%, x=0, n) ;
end proc:
g := proc(n, m)
add(binomial(m, k)*(-1)^(m-k)*z(n, k), k=0..m) ;
end proc:
seq(seq(g(n, m), m=0..n), n=0..12) ;
MATHEMATICA
z[n_, m_] := Module[{kmax, s}, kmax = n+1; s = Sum[(-1)^k*(1-(1-x^k)^m)/ (1-x^k)^m, {k, 1, kmax}]; SeriesCoefficient[1/(1+s), {x, 0, n}]];
g[n_, m_] := Sum[Binomial[m, k]*(-1)^(m-k)*z[n, k], {k, 0, m}];
Table[Table[g[n, m], {m, 0, n}], {n, 0, 10}] // Flatten (* Jean-François Alcover, Oct 28 2023, after R. J. Mathar's program *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. J. Mathar, Jul 15 2016
STATUS
approved