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4th differences of Bell numbers.
3

%I #19 Aug 04 2015 15:43:00

%S 4,15,67,322,1657,9089,52922,325869,2114719,14418716,103004851,

%T 769052061,5987339748,48506099635,408157244967,3561086589202,

%U 32164670915029,300324194090773,2894932531218482,28773297907499129

%N 4th differences of Bell numbers.

%H Chai Wah Wu, <a href="/A011967/b011967.txt">Table of n, a(n) for n = 0..250</a>

%H Cohn, Martin; Even, Shimon; Menger, Karl, Jr.; Hooper, Philip K.; <a href="http://www.jstor.org/stable/2310780">On the Number of Partitionings of a Set of n Distinct Objects</a>, Amer. Math. Monthly 69 (1962), no. 8, 782--785. MR1531841.

%H Cohn, Martin; Even, Shimon; Menger, Karl, Jr.; Hooper, Philip K.; <a href="/A011965/a011965.pdf">On the Number of Partitionings of a Set of n Distinct Objects</a>, Amer. Math. Monthly 69 (1962), no. 8, 782--785. MR1531841. [Annotated scanned copy]

%H Jocelyn Quaintance and Harris Kwong, <a href="http://www.emis.de/journals/INTEGERS/papers/n29/n29.Abstract.html">A combinatorial interpretation of the Catalan and Bell number difference tables</a>, Integers, 13 (2013), #A29.

%t Differences[BellB[Range[0, 50]], 4] (* _Vladimir Joseph Stephan Orlovsky_, May 25 2011 *)

%o (Python)

%o # requires python 3.2 or higher. Otherwise use def'n of accumulate in python docs.

%o from itertools import accumulate

%o A011967_list, blist, b = [4], [5, 7, 10, 15], 15

%o for _ in range(250):

%o ....blist = list(accumulate([b]+blist))

%o ....b = blist[-1]

%o ....A011967_list.append(blist[-5]) # _Chai Wah Wu_, Sep 20 2014

%Y Cf. A000110, A005493, A011965, A011966, A106436.

%K nonn

%O 0,1

%A _N. J. A. Sloane_.