cp's OEIS Frontend

A244489 Triangle read by rows: T(n,k) = Sum_{j=k..n} binomial(n,j)*Stirling_2(j,k)*Bell(n-j), where Bell(n) = A000110(n), for n >= 1, 0 <= k <= n-1.

%I A244489 #22 Oct 09 2018 05:41:33
%S A244489 1,2,3,5,10,6,15,37,31,10,52,151,160,75,15,203,674,856,520,155,21,877,
%T A244489 3263,4802,3556,1400,287,28,4140,17007,28337,24626,11991,3290,490,36,
%U A244489 21147,94828,175896,174805,101031,34671,6972,786,45,115975,562595,1146931,1279240,853315,350889,88977,13620,1200,55
%N A244489 Triangle read by rows: T(n,k) = Sum_{j=k..n} binomial(n,j)*Stirling_2(j,k)*Bell(n-j), where Bell(n) = A000110(n), for n >= 1, 0 <= k <= n-1.
%H A244489 J. East, R. D. Gray, <a href="http://arxiv.org/abs/1404.2359">Idempotent generators in finite partition monoids and related semigroups</a>, arXiv preprint arXiv:1404.2359 [math.GR], 2014.
%e A244489 Triangle begins:
%e A244489 1
%e A244489 2 3
%e A244489 5 10 6
%e A244489 15 37 31 10
%e A244489 52 151 160 75 15
%e A244489 203 674 856 520 155 21
%e A244489 877 3263 4802 3556 1400 287 28
%e A244489 4140 17007 28337 24626 11991 3290 490 36
%e A244489 ...
%t A244489 T[n_, k_] := Sum[Binomial[n, j] StirlingS2[j, k] BellB[n-j], {j, k, n}];
%t A244489 Table[T[n, k], {n, 1, 10}, {k, 0, n-1}] // Flatten (* _Jean-François Alcover_, Oct 09 2018 *)
%Y A244489 Same as A049020 (which is the main entry for this triangle) except the present sequence has an extra 1 at the end of each row. - _R. J. Mathar_ and _N. J. A. Sloane_, May 17 2016
%K A244489 nonn,tabl
%O A244489 1,2
%A A244489 _N. J. A. Sloane_, Jul 04 2014