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A122850 Exponential Riordan array (1, sqrt(1+2x)-1). 3
1, 0, 1, 0, -1, 1, 0, 3, -3, 1, 0, -15, 15, -6, 1, 0, 105, -105, 45, -10, 1, 0, -945, 945, -420, 105, -15, 1, 0, 10395, -10395, 4725, -1260, 210, -21, 1, 0, -135135, 135135, -62370, 17325, -3150 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Inverse of number triangle A122848. Entries are Bessel polynomial coefficients. Row sums are A000806.

Also the inverse Bell transform of the sequence "g(n) = 1 if n<2 else 0". For the definition of the Bell transform see A264428. - Peter Luschny, Jan 19 2016

LINKS

Table of n, a(n) for n=0..41.

M. Janjic, Some classes of numbers and derivatives, JIS 12 (2009) 09.8.3

FORMULA

T(n,k) = (-1)^(n-k)*A132062(n,k). - Philippe Deléham, Nov 06 2011

Triangle equals the matrix product A039757*A008277. Dobinski-type formula for the row polynomials: R(n,x) = exp(-x)*sum {k = 0..inf} k*(k-1)*(k-3)*(k-5)*...*(k-1-2*(n-1))*x^k/k!. Cf. A001497. - Peter Bala, Jun 23 2014

EXAMPLE

Triangle begins

1

0 1

0 -1 1

0 3 -3 1

0 -15 15 -6 1

0 105 -105 45 -10 1

0 -945 945 -420 105 -15 1

0 10395 -10395 4725 -1260 210 -21 1

0 -135135 135135 -62370 17325 -3150 378 -28 1

0 2027025 -2027025 945945 -270270 51975 -6930 630 -36 1

0 -34459425 34459425 -16216200 4729725 -945945 135135 -13860 990 -45 1

MAPLE

# The function BellMatrix is defined in A264428.

BellMatrix(n -> (-1)^n*doublefactorial(2*n-1), 9); # Peter Luschny, Jan 27 2016

PROG

(Sage)

# The function bell_matrix is defined in A264428.

bell_matrix(lambda n: 1 if n<2 else 0, 12).inverse() # Peter Luschny, Jan 19 2016

CROSSREFS

Cf. A000806, A001497, A008277, A039757, A122848, A132062.

Sequence in context: A265608 A184962 A264436 * A132062 A065547 A143333

Adjacent sequences:  A122847 A122848 A122849 * A122851 A122852 A122853

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Sep 14 2006

STATUS

approved

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Last modified December 7 23:12 EST 2016. Contains 278900 sequences.