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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

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)).

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 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

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

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Last modified July 22 02:20 EDT 2019. Contains 325210 sequences. (Running on oeis4.)