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A117716 Triangle T(n,m) read by rows: the coefficient [x^n] of x^2/(1-m*x-x^3) in row n, columns 1<=m<=n+1. 2
0, 0, 0, 1, 1, 1, 1, 2, 3, 4, 1, 4, 9, 16, 25, 2, 9, 28, 65, 126, 217, 3, 20, 87, 264, 635, 1308, 2415, 4, 44, 270, 1072, 3200, 7884, 16954, 32960, 6, 97, 838, 4353, 16126, 47521, 119022, 264193, 534358, 9, 214, 2601, 17676, 81265, 286434, 835569, 2117656 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Table of n, a(n) for n=0..52.

EXAMPLE

0

0, 0

1, 1, 1

1, 2, 3, 4

1, 4, 9, 16, 25

2, 9, 28, 65, 126, 217

3, 20, 87, 264, 635, 1308, 2415

4, 44, 270, 1072, 3200, 7884, 16954, 32960

MAPLE

A117716 := proc(n, m)

x^2/(1-m*x-x^3) ;

if n < 0 then

0;

else

coeftayl(%, x=0, n) ;

end if;

end proc: # R. J. Mathar, May 14 2013

MATHEMATICA

(* define the polynomial*) p[x_] = x/(1 - m*x - x3); (* Taylor derivative expansion of the polynomial*) a = Table[Flatten[{{p[0]}, Table[Coefficient[Series[p[x], {x, 0, 30}], x^n], {n, 1, 10}]}], {m, 1, 10}] (*antidiagonal expansion to give triangular function*) b = Join[{{0}}, Delete[Table[Table[a[[n]][[m]], {n, 1, m + 1}], {m, 0, 9}], 1]] Flatten[b]

CROSSREFS

Cf. A000930 (column 0), A008998 (column 1), A052541 (column 2), A052927 (column 3), A001093 (row 5), A185065 (row 6), A117715, A117724.

Sequence in context: A352724 A248723 A117742 * A211234 A359122 A240185

Adjacent sequences: A117713 A117714 A117715 * A117717 A117718 A117719

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Apr 13 2006, corrected Apr 15 2006

STATUS

approved

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Last modified January 29 07:25 EST 2023. Contains 359915 sequences. (Running on oeis4.)