A331528
COMMENTS の数式を確認しておく。
(00:00) gp > {b(n, k) = sum(j=0, n, (-1)^(n-j)*j^k*binomial(n, j)*binomial(n+j, j))}
%1 = (n,k)->sum(j=0,n,(-1)^(n-j)*j^k*binomial(n,j)*binomial(n+j,j))
(00:01) gp > for(n=0, 20, print1(b(n,0)-1, ", "))
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
(00:01) gp > for(n=0, 20, print1(b(n,1)-1/1!*n*(n+1), ", "))
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
(00:01) gp > for(n=0, 20, print1(b(n,2)-1/2!*n^2*(n+1)^2, ", "))
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
(00:02) gp > for(n=0, 20, print1(b(n,3)-1/3!*n^2*(n+1)^2*(n^2+n+1), ", "))
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
(00:02) gp > for(n=0, 20, print1(b(n,4)-1/4!*n^3*(n+1)^3*(n^2+n+4), ", "))
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
(00:02) gp > for(n=0, 20, print1(b(n,5)-1/5!*n^2*(n+1)^2*(n^6+3*n^5+13*n^4+21*n^3+18*n^2+8*n-4), ", "))
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
(00:02) gp > for(n=0, 20, print1(b(n,6)-1/6!*n^3*(n+1)^3*(n^2+n+4)*(n^4+2*n^3+17*n^2+16*n-6), ", "))
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
(00:02) gp >
