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A099569 Riordan array ((1+x)^2-x^3)/(1+x)^3, 1/(1+x)). 2
1, -1, 1, 1, -2, 1, -2, 3, -3, 1, 4, -5, 6, -4, 1, -7, 9, -11, 10, -5, 1, 11, -16, 20, -21, 15, -6, 1, -16, 27, -36, 41, -36, 21, -7, 1, 22, -43, 63, -77, 77, -57, 28, -8, 1, -29, 65, -106, 140, -154, 134, -85, 36, -9, 1, 37, -94, 171, -246, 294, -288, 219, -121, 45, -10, 1, -46, 131, -265, 417, -540, 582, -507, 340, -166, 55 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Inverse matrix of A099567. Row sums are A099570.

LINKS

Table of n, a(n) for n=0..75.

FORMULA

Columns have g.f. ((1+x)^2-x^3)/(1+x)^3(x/(1+x))^k.

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

EXAMPLE

Rows begin {1}, {-1,1}, {1,-2,1}, {-2,3,-3,1}, {4,-5,6,-4,1},...

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) + add((i-2)*C(n-i, n-k-i), i = 3..n)), k = 0..n);

end do; # Peter Bala, Mar 21 2018

CROSSREFS

Cf. A099570, A099567.

Sequence in context: A202191 A052250 A333878 * A191579 A097724 A091836

Adjacent sequences:  A099566 A099567 A099568 * A099570 A099571 A099572

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Oct 22 2004

STATUS

approved

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Last modified June 13 00:57 EDT 2021. Contains 344980 sequences. (Running on oeis4.)