The On-Line Encyclopedia of Integer Sequences (OEIS)

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A086634

Triangle of coefficients, read by rows, where T(n,k) is the coefficient of x^n*y^k in f(x,y) that satisfies f(x,y) = (1+x) - x^2*(1+x)^3 + xy*f(x,y)^3.
(history; published version)

#3 by Russ Cox at Fri Mar 30 18:36:38 EDT 2012

AUTHOR

_Paul D. Hanna (pauldhanna(AT)juno.com), _, Jul 25 2003

Discussion

Fri Mar 30

18:36

OEIS Server: https://oeis.org/edit/global/213

#2 by N. J. A. Sloane at Sat Nov 10 03:00:00 EST 2007

KEYWORD

sign,tabl,new

AUTHOR

Paul D . Hanna (pauldhanna(AT)juno.com), Jul 25 2003

#1 by N. J. A. Sloane at Sat Sep 13 03:00:00 EDT 2003

NAME

Triangle of coefficients, read by rows, where T(n,k) is the coefficient of x^n*y^k in f(x,y) that satisfies f(x,y) = (1+x) - x^2*(1+x)^3 + xy*f(x,y)^3.

DATA

1, 1, 1, -1, 3, 3, -3, 0, 15, 12, -3, -14, 15, 84, 55, -1, -27, -75, 168, 495, 273, 0, -9, -270, -336, 1485, 3003, 1428, 0, 47, -252, -2352, -825, 12012, 18564, 7752, 0, 93, 525, -4032, -18315, 6006, 92820, 116280, 43263, 0, 69, 1875, 2940, -49005, -129129, 129948, 697680, 735471, 246675

OFFSET

0,5

COMMENTS

The main diagonal gives A001764 ( C(3n,n)/(2n+1) ). First column is given by g.f: (1+x) - x^2*(1+x)^3. Antidiagonal sums result in binomial {1,1,0,...}.

EXAMPLE

Rows begin:

{1},

{1,1},

{-1,3,3},

{-3,0,15,12},

{-3,-14,15,84,55},

{-1,-27,-75,168,495,273},

{0,-9,-270,-336,1485,3003,1428},

{0,47,-252,-2352,-825,12012,18564,7752}, ...

CROSSREFS

Cf. A086635 (row sums), A086632.

KEYWORD

sign,tabl

AUTHOR

Paul D Hanna (pauldhanna(AT)juno.com), Jul 25 2003

STATUS

approved