login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A102051 Matrix inverse of triangle A101275 (number of Schröder 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)).

T(n,m) = (-1)^(n-m)*(2*m+1)*Sum_{k=0..n} C(k,n-k)*C(2*k,k-m)/(m+k+1). - Vladimir Kruchinin, Apr 18 2015

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)}

(Maxima)

T(n, m):=(-1)^(n-m)*(2*m+1)*(sum((binomial(k, n-k)*binomial(2*k, k-m))/(m+k+1), k, 0, n)); /* Vladimir Kruchinin, Apr 18 2015 */

CROSSREFS

Cf. A101275, A006139, A052709, A102052, A102053, A039599.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 7 17:16 EST 2016. Contains 278890 sequences.