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A101413 Triangle read by rows: Coefficients of characteristic polynomials of lower triangular matrix of Catalan numbers. 0
1, -1, 1, -3, 2, 1, -8, 17, -10, 1, -22, 129, -248, 140, 1, -64, 1053, -5666, 10556, -5880, 1, -196, 9501, -144662, 758468, -1399272, 776160, 1, -625, 93585, -4220591, 62818466, -326782044, 601063848, -332972640, 1, -2055, 987335, -138047141, 6098263596, -90157188424, 467899386768 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Roots of n-th characteristic polynomial are the first n Catalan numbers (A000108). Second column of triangle is A014138(n) (Partial sums of Catalan numbers.)

LINKS

Table of n, a(n) for n=1..42.

EXAMPLE

Generation of the triangle:

We begin with A050166 (triangle)

1

1 2

1 4 5

1 6 14 14

1 8 27 48 42

...

and get polynomials

x - 1

x^2 - 3*x + 2

x^3 - 8*x^2 + 17*x - 10

x^4 - 22*x^3 + 129*x^2 - 248*x + 140

x^5 - 64*x^4 + 1053*x^3 - 5666*x^2 + 10556*x - 5880

...

PROG

(PARI) a(n, k)=binomial(2*n+1, k)*2*(n-k+1)/(2*n-k+2); CM(n)=M=matrix(n, n); for(l=0, n-1, for(k=0, l, M[l+1, k+1]=a(l, k))); M for(i=1, 10, print(charpoly(CM(i)))) for(i=1, 10, print(round(real(polroots(charpoly(CM(i)))))))

CROSSREFS

Cf. A000108, A014138.

Sequence in context: A203992 A204019 A196846 * A101908 A290310 A086963

Adjacent sequences:  A101410 A101411 A101412 * A101414 A101415 A101416

KEYWORD

sign,tabl

AUTHOR

Lambert Klasen (lambert.klasen(AT)gmx.net) and Gary W. Adamson, Jan 29 2005

STATUS

approved

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Last modified February 19 09:33 EST 2020. Contains 332041 sequences. (Running on oeis4.)