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A259666 Number of n X n prime Tesler matrices. 2
1, 1, 3, 18, 181, 2788, 62590, 1989540, 87979661, 5349559222, 443306080232, 49679250634068, 7473835936432840, 1498682325685621140, 397803907069442925517, 138847938093177059278212, 63325340852730727078521540, 37513306417359729218973719474, 28701720575221087513434901774347 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Number of n X n upper triangular matrices A of nonnegative integers such that a_1i + a_2i + ... + a_{i-1,i} - a_ii - a_{i,i+1} - ... - a_in = -1, whose simple graph G with vertices 1,2,3..,n and edges (i,j) if a_ij>0 is connected.

LINKS

Table of n, a(n) for n=1..19.

A. Garsia and J. Haglund, A polynomial expression for the character of diagonal harmonics, Ann. Comb., to appear, 2015.

FORMULA

E.g.f.: 1 + log( 1+ sum(n>=1, A008608(n) * x^n / n! ) ).

EXAMPLE

Example: For n =3 the a(3) = 3 matrices are [[0,1,0],[0,1,1],[0,0,2]], [[0,1,0],[0,0,2],[0,0,3]], [[0,0,1],[0,0,1],[0,0,3]].

E.g.f.: 1 + x+(1/2)*x^2+(3/6)*x^3+(18/24)*x^4+(181/120)*x^5+(2788/720)*x^6 + ...

MAPLE

multcoeff:=proc(n, f, coeffv, k)

   local i, currcoeff;

   currcoeff:=f;

   for i from 1 to n do

      currcoeff:=`if`(coeffv[i]=0, coeff(series(currcoeff, x[i], k), x[i], 0), coeff(series(currcoeff, x[i], k), x[i]^coeffv[i]));

   end do;

   return currcoeff;

end proc:

F:=n->mul(mul((1-x[i]*x[j]^(-1))^(-1), j=i+1..n), i=1..n):

b := n -> multcoeff(n+1, F(n+1), [seq(1, i=1..n), -n], n+2):

sa := 1 + log(1+ add(b(n)*x^n/n!, n=1..7)):

a := n -> n!*coeff(series(sa, x, n+1), x, n):

seq(a(i), i=1..6);

CROSSREFS

Cf. A008608, A259485.

Sequence in context: A108994 A006472 A132853 * A084879 A141118 A033030

Adjacent sequences:  A259663 A259664 A259665 * A259667 A259668 A259669

KEYWORD

nonn

AUTHOR

Alejandro H. Morales, Jul 02 2015

EXTENSIONS

a(15)-a(19) from Alois P. Heinz, Jul 05 2015

STATUS

approved

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Last modified October 19 03:36 EDT 2018. Contains 316330 sequences. (Running on oeis4.)