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A160486 Triangle of polynomial coefficients related to the o.g.f.s. of the RBS1 polynomials 4
1, 1, 1, 1, 18, 5, 1, 179, 479, 61, 1, 1636, 18270, 19028, 1385, 1, 14757, 540242, 1949762, 1073517, 50521, 1, 132854, 14494859, 137963364, 241595239, 82112518, 2702765 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

As we showed in A160485 the n-th term of the coefficients of matrix row BS1[1-2*m,n] for m = 1 , 2, 3, .. , can be generated with the RBS1(1-2*m,n) polynomials.

We define the o.g.f.s. of these polynomials by GFRBS1(z,1-2*m) = sum(RBS1(1-2*m,n)*z^(n-1), n=1..infinity) for m = 1, 2, 3, .. . The general expression of these o.g.f.s. is GFRBS1(z,1-2*m) = (-1)*RB(z,1-2*m)/(z-1)^m.

The RB(z,1-2*m) polynomials lead to a triangle that is a subtriangle of the 'double triangle' A008971. The even rows of the latter triangle are identical to the rows of our triangle.

The Maple program given below is derived from the one given in A008971.

LINKS

Table of n, a(n) for n=1..28.

EXAMPLE

The first few rows of the triangle are:

[1]

[1, 1]

[1, 18, 5]

[1, 179, 479, 61]

[1, 1636, 18270, 19028, 1385]

The first few RB(z,1-2*m) polynomials are:

RB(z,-1) = 1

RB(z,-3) = z+1

RB(z,-5) = z^2+18*z+5

RB(z,-7) = z^3+179*z^2+479*z+61

The first few GFRBS1(z,1-2*m) are:

GFRBS1(z,-1) = (-1)*(1)/(z-1)

GFRBS1(z,-3) = (-1)*(z+1)/(z-1)^2

GFRBS1(z,-5) = (-1)*(z^2+18*z+5)/(z-1)^3

GFRBS1(z,-7) = (-1)*(z^3+179*z^2+479*z+61)/(z-1)^4

MAPLE

nmax:=15; G := sqrt(1-t)/(sqrt(1-t)*cosh(x*sqrt(1-t))-sinh(x*sqrt(1-t))): Gser := simplify(series(G, x=0, nmax+1)): for m from 0 to nmax do P[m] := sort(expand(m!* coeff(Gser, x, m))) od: nmx := floor(nmax/2); for n from 0 to nmx do for k from 0 to nmx-1 do A(n+1, n+1-k) := coeff(P[2*n], t, n-k) od: od: seq(seq(A(n, m), m=1..n), n=1..nmx);

CROSSREFS

Cf. A160480 and A160485.

The row sums equal A010050.

This triangle is a sub-triangle of A008971.

A000340(2*n-2), A000363(2*n+2) and A000507(2*n+4) equal the second, third and fourth left hand columns.

The first right hand column equals the Euler numbers A000364.

Sequence in context: A059654 A080694 A040314 * A040312 A214893 A065909

Adjacent sequences:  A160483 A160484 A160485 * A160487 A160488 A160489

KEYWORD

easy,nonn,tabl

AUTHOR

Johannes W. Meijer, May 24 2009, Sep 19 2012

STATUS

approved

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Last modified December 14 07:39 EST 2018. Contains 318090 sequences. (Running on oeis4.)