

A129334


Triangle T(n,k) read by rows: inverse of the matrix PE = exp(P)/exp(1) given in A011971.


0



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, 50, 72, 252, 112, 70, 56, 0, 8, 1, 267, 450, 324, 756, 252, 126, 84, 0, 9, 1, 413, 2670, 2250, 1080, 1890, 504, 210, 120
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OFFSET

0,5


COMMENTS

The structure of the triangle is A[r,c] = A000587(1+(rc))*binomial(r1,c1) where row index r and columnindex 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(1cxexp(x)).


LINKS

Table of n, a(n) for n=0..62.
S. de Wannemacker, T. Laffey and R. Osburn, On a conjecture of Wilf


FORMULA

Let P be the lowertriangular Pascalmatrix, PE = exp(PI) 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


EXAMPLE

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,


CROSSREFS

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 * A116399 A116405 A281048
Adjacent sequences: A129331 A129332 A129333 * A129335 A129336 A129337


KEYWORD

easy,tabl,sign


AUTHOR

Gottfried Helms, Apr 08 2007


EXTENSIONS

Edited by Ralf Stephan, May 12 2007


STATUS

approved



