A122433 Riordan array ((1+x)^2,x/(1+x)).

1, 2, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, -1, 1, 0, 0, 0, 1, -2, 1, 0, 0, 0, -1, 3, -3, 1, 0, 0, 0, 1, -4, 6, -4, 1, 0, 0, 0, -1, 5, -10, 10, -5, 1, 0, 0, 0, 1, -6, 15, -20, 15, -6, 1, 0, 0

Offset

0,2

Comments

Row sums are C(3,n). Diagonal sums are A122434. Product of A007318 and A122432. Inverse is Riordan array ((1-x)^2,x/(1-x)).

Links

Table of n, a(n) for n=0..56.

Formula

T(n,k) = (-1)^(n+k)*(C(n, n-k) - 3*C(n-1, n-k-1) + 3*C(n-2, n-k-2) - C(n-3, n-k-3)), where C(n,k) = n!/(k!*(n-k)!) for 0 <= k <= n, otherwise 0. - Peter Bala, Mar 21 2018

Example

Triangle begins
1,
2, 1,
1, 1, 1,
0, 0, 0, 1,
0, 0, 0, -1, 1,
0, 0, 0, 1, -2, 1,
0, 0, 0, -1, 3, -3, 1,
0, 0, 0, 1, -4, 6, -4, 1,
0, 0, 0, -1, 5, -10, 10, -5, 1,
0, 0, 0, 1, -6, 15, -20, 15, -6, 1,
0, 0, 0, -1, 7, -21, 35, -35, 21, -7, 1

Maple

C := proc (n, k) if 0 <= k and k <= n then factorial(n)/(factorial(k)*factorial(n-k)) else 0 end if;
end proc:
for n from 0 to 10 do
seq((-1)^(n+k)*(C(n, n-k)-3*C(n-1, n-k-1)+3*C(n-2, n-k-2)-C(n-3, n-k-3)), k = 0..n);
end do; # Peter Bala, Mar 21 2018

Crossrefs

Cf. A007318, A122432.

Sequence in context: A316866 A277007 A160380 * A056977 A309144 A085425

Adjacent sequences: A122430 A122431 A122432 * A122434 A122435 A122436

Keyword

easy,sign,tabl

Author

Paul Barry, Sep 04 2006

Status

approved