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

Double-exponential generating function: sum_{n, k} a(n-k, k) x^n/n! y^k/k! = exp(exp{x+y}-1-x). a(n,k) = Sum_{i=k..n} (-1)^(n-i)*binomial(n-k,i-k)*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, A011965-A011967, A191099, A000298, A011968-A011970.

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

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Last modified November 29 00:06 EST 2014. Contains 250479 sequences.