OFFSET
0,8
COMMENTS
First negative value appears at T(11,5). - Indranil Ghosh, Mar 04 2017
LINKS
Indranil Ghosh, Rows 0..100, flattened
FORMULA
EXAMPLE
0;
0, 0;
0, 1, 1;
0, 2, 6, 4;
0, 3, 11, 22, 13;
0, 4, 20, 45, 75, 41;
0, 5, 29, 110, 190, 261, 131;
0, 6, 42, 154, 560, 826, 938, 428;
MAPLE
T := proc(n, k) binomial(n, k)*binomial(2*k, k)/(k+1) - add((-1)^j*(1-j)^n /(j!*(k-j)!), j = 0..k) end:
for n from 0 to 12 do seq(T(n, k), k=0..n) od;
MATHEMATICA
Flatten[Table[(Binomial[n, k] * Binomial[2k, k] / (k+1)) - Sum[(-1)^j*(1-j)^n*Binomial[k, j]/k!, {j, 0, k}], {n, 0, 10}, {k, 0, n}]] (* Indranil Ghosh, Mar 04 2017 *)
PROG
(PARI)
tabl(nn) = {for (n=0, nn, for (k=0, n, print1((binomial(n, k)*binomial(2*k, k)/(k+1))-sum(j=0, k, (-1)^j*(1-j)^n*binomial(k, j)/k!), ", ", ); ); print(); ); };
tabl(10); \\ Indranil Ghosh, Mar 04 2017
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Peter Luschny, Oct 02 2014
STATUS
approved