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A202191 Triangle T(n,m) = coefficient of x^n in expansion of [x/(1-x-x^3)]^m = sum(n>=m, T(n,m) x^n). 1
1, 1, 1, 1, 2, 1, 2, 3, 3, 1, 3, 6, 6, 4, 1, 4, 11, 13, 10, 5, 1, 6, 18, 27, 24, 15, 6, 1, 9, 30, 51, 55, 40, 21, 7, 1, 13, 50, 94, 116, 100, 62, 28, 8, 1, 19, 81, 171, 234, 231, 168, 91, 36, 9, 1, 28, 130, 303, 460, 505, 420, 266, 128, 45, 10, 1, 41, 208 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

The matrix inverse starts

1;

-1,1;

1,-2,1;

-2,3,-3,1;

5,-6,6,-4,1;

-11,15,-13,10,-5,1;

24,-36,33,-24,15,-6,1;

-57,84,-84,63,-40,21,-7,1;

141,-204,208,-168,110,-62,28,-8,1. - R. J. Mathar, Mar 15 2013

LINKS

Table of n, a(n) for n=1..68.

FORMULA

T(n,m)=sum(k=0..n-m, binomial(k,(n-m-k)/2)*binomial(m+k-1,m-1)*((-1)^(n-m-k)+1))/2.

EXAMPLE

1

1, 1,

1, 2, 1,

2, 3, 3, 1,

3, 6, 6, 4, 1,

4, 11, 13, 10, 5, 1,

6, 18, 27, 24, 15, 6, 1

MAPLE

A202191 := proc(n, k)

    (x/(1-x-x^3))^k ;

    coeftayl(%, x=0, n) ;

end proc: # R. J. Mathar, Mar 15 2013

PROG

(Maxima)

T(n, m):=sum(binomial(k, (n-m-k)/2)*binomial(m+k-1, m-1)*((-1)^(n-m-k)+1), k, 0, n-m)/2;

CROSSREFS

Sequence in context: A267177 A099567 A140530 * A052250 A099569 A191579

Adjacent sequences:  A202188 A202189 A202190 * A202192 A202193 A202194

KEYWORD

nonn,tabl

AUTHOR

Vladimir Kruchinin, Dec 14 2011

STATUS

approved

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Last modified February 17 02:33 EST 2019. Contains 320200 sequences. (Running on oeis4.)