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A102051 Matrix inverse of triangle A101275 (number of Schroeder paths). 2
1, -1, 1, 3, -4, 1, -9, 15, -7, 1, 31, -58, 36, -10, 1, -113, 229, -170, 66, -13, 1, 431, -924, 775, -372, 105, -16, 1, -1697, 3795, -3481, 1939, -691, 153, -19, 1, 6847, -15822, 15542, -9674, 4072, -1154, 210, -22, 1, -28161, 66801, -69276, 47012, -22446, 7606, -1788, 276, -25, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Row sums are {1,0,0,0...}. Absolute row sums form A006139. Column 0 forms signed A052709. Column 1 forms A102052. Column 2 forms A102053.

LINKS

Table of n, a(n) for n=0..54.

FORMULA

G.f.: 2/(1+y+(1-y)*sqrt(1+4*x-4*x^2)).

EXAMPLE

Rows begin:

[1],

[ -1,1],

[3,-4,1],

[ -9,15,-7,1],

[31,-58,36,-10,1],

[ -113,229,-170,66,-13,1],

[431,-924,775,-372,105,-16,1],

[ -1697,3795,-3481,1939,-691,153,-19,1],

[6847,-15822,15542,-9674,4072,-1154,210,-22,1],...

Matrix inverse equals triangle A101275:

[1],

[1,1],

[1,4,1],

[1,13,7,1],

[1,44,34,10,1],...

PROG

(PARI) {T(n, k)=polcoeff(polcoeff(2/(2*y+(1-y)*(1+sqrt(1+4*x-4*x^2+x*O(x^n)))), n)+y*O(y^k), k)}

CROSSREFS

Cf. A101275, A006139, A052709, A102052, A102053.

Sequence in context: A010611 A136158 A164948 * A078068 A054649 A138263

Adjacent sequences:  A102048 A102049 A102050 * A102052 A102053 A102054

KEYWORD

sign,tabl

AUTHOR

Paul D. Hanna, Dec 27 2004

STATUS

approved

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Last modified April 19 17:29 EDT 2014. Contains 240767 sequences.