

A106436


Difference array of Bell numbers A000110 read by antidiagonals.


11



1, 0, 1, 1, 1, 2, 1, 2, 3, 5, 4, 5, 7, 10, 15, 11, 15, 20, 27, 37, 52, 41, 52, 67, 87, 114, 151, 203, 162, 203, 255, 322, 409, 523, 674, 877, 715, 877, 1080, 1335, 1657, 2066, 2589, 3263, 4140, 3425, 4140, 5017, 6097, 7432, 9089, 11155, 13744
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OFFSET

0,6


COMMENTS

Essentially Aitken's array A011971 with first column A000296.


REFERENCES

Jocelyn Quaintance and Harris Kwong, A combinatorial interpretation of the Catalan and Bell number difference tables, Integers, 13 (2013), #A29.


LINKS

Table of n, a(n) for n=0..52.


FORMULA

Doubleexponential generating function: sum_{n, k} a(nk, k) x^n/n! y^k/k! = exp(exp{x+y}1x). a(n,k) = Sum_{i=k..n} (1)^(ni)*binomial(nk,ik)*Bell(i).  Vladeta Jovovic, Oct 14 2006


EXAMPLE

1; 0, 1; 1, 1, 2; 1, 2, 3, 5; 4, 5, 7, 10, 15; 11, 15, 20, 27, 37, 52; ...


CROSSREFS

Cf. A000110.
Diagonals give A005493, A011965A011967, A191099, A000298, A011968A011970.
Sequence in context: A059346 A076492 A127462 * A075758 A125596 A204994
Adjacent sequences: A106433 A106434 A106435 * A106437 A106438 A106439


KEYWORD

nonn,easy,tabl


AUTHOR

Philippe Deléham, May 29 2005


STATUS

approved



