0,5

The structure of the triangle is A[r,c] = A000587(1+(r-c))*binomial(r-1,c-1) where row index r and column-index c start at 1.

Coefficients of polynomials defined recursively: P(0,x)=1, P(n+1,x)=x*P(n,x)-P(n,x+1). All generated polynomials appear to be irreducible. Polynomials evaluated at x=c give sequences with e.g.f. exp(1-cx-exp(-x)).

S. de Wannemacker, T. Laffey and R. Osburn, On a conjecture of Wilf

Let P be the lower-triangular Pascal-matrix, PE = exp(P-I) a matrix- exponential in exact integer arithmetic (or PE = lim exp(P)/exp(1) as limit of the exponential) then A= PE^-1 and a(n) = A[n, read sequentially]. - Gottfried Helms, Apr 08 2007

Triangle starts:

1,

-1,1,

0,-2,1,

1,0,-3,1,

1,4,0,-4,1,

-2,5,10,0,-5,1,

-9,-12,15,20,0,-6,1,

-9,-63,-42,35,35,0,-7,1,

First column is A000587 (Uppuluri Carpenter numbers) which is also the negative of the row sums (=P(n, 1)). Polynomials evaluated at 2 are A074051, at -1 A109747.

Sequence in context: A136481 A100218 A098599 this_sequence A116399 A116405 A029352

Adjacent sequences: A129331 A129332 A129333 this_sequence A129335 A129336 A129337

easy,tabl,sign

Gottfried Helms (helms(AT)uni-kassel.de), Apr 08 2007

Edited by Ralf Stephan, May 12 2007