A107102 Matrix inverse of A100862.

1, -1, 1, 2, -3, 1, -7, 12, -6, 1, 37, -67, 39, -10, 1, -266, 495, -310, 95, -15, 1, 2431, -4596, 3000, -1010, 195, -21, 1, -27007, 51583, -34566, 12320, -2660, 357, -28, 1, 353522, -680037, 463981, -171766, 39795, -6062, 602, -36, 1, -5329837, 10306152, -7124454, 2709525, -658791, 108927, -12432, 954

Offset: 0

Author

Paul D. Hanna, May 21 2005

Keywords

• sign
• tabl

Comments

Column 0 is signed A001515 (Bessel polynomial). Column 1 is A107103. Row sums are zeros for n>0. Absolute row sums form A107104, which equals 2*A043301(n-1) for n>0.

The row polynomials p_n(x) of this entry are (-1)^n B_n(1-x), where B_n(x) are the modified Carlitz-Bessel polynomials of A001497, e,g, (-1)^2 B_2(1-x) = (1-x) + (1-x)^2 = 2 - 3 x + x^2 = p_2(x). - Tom Copeland, Oct 10 2016

Examples

			Triangle begins:
1;
-1,1;
2,-3,1;
-7,12,-6,1;
37,-67,39,-10,1;
-266,495,-310,95,-15,1;
2431,-4596,3000,-1010,195,-21,1;
-27007,51583,-34566,12320,-2660,357,-28,1; ...
and is the matrix inverse of A100862:
1;
1,1;
1,3,1;
1,6,6,1;
1,10,21,10,1;
1,15,55,55,15,1; ...
		

Crossrefs

Cf. A100862, A001515, A043301, A107103, A107104.

Cf. A001497.

Programs

PARI

{T(n,k)=local(X=x+x*O(x^n),Y=y+y*O(y^n));(matrix(n+1,n+1,m,j,if(m>=j, (m-1)!*polcoeff(polcoeff(exp(X+Y*X^2/2+X*Y),m-1,x),j-1,y)))^-1)[n+1,k+1]}

Formula

E.g.f.: exp((1-y)*(1-sqrt(1+2*x))). [Vladeta Jovovic, Dec 13 2008]