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A109978 Inverse binomial transform of number-theoretic triangle A109974. 1
1, 1, 1, -1, 1, 1, 2, -2, 2, 1, -5, 5, -4, 5, 1, 13, -14, 11, -7, 12, 1, -33, 40, -35, 20, -5, 27, 1, 80, -111, 113, -77, 21, 34, 58, 1, -184, 293, -350, 294, -144, -27, 238, 121, 1, 402, -731, 1021, -1042, 716, -249, -153, 1063, 248, 1, -840, 1726, -2796, 3409, -2982, 1755, -724, 318, 4037, 503, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

First column is expansion of bracket function A001659.

LINKS

Table of n, a(n) for n=1..66.

FORMULA

T(n, k)=sum{j=1..n, (-1)^(n-j)C(n-1, j-1)*if(k<=j, sigma(k-1, j-k+1), 0)} [offset (1, 1)]

EXAMPLE

Rows begin

1;

1,1;

-1,1,1;

2,-2,2,1;

-5,5,-4,5,1;

13,-14,11,-7,12,1;

-33,40,-35,20,-5,27,1;

CROSSREFS

Sequence in context: A261360 A184242 A307739 * A114293 A295691 A285183

Adjacent sequences:  A109975 A109976 A109977 * A109979 A109980 A109981

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Jul 06 2005

STATUS

approved

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Last modified September 16 12:34 EDT 2019. Contains 327098 sequences. (Running on oeis4.)