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%I #29 Dec 18 2023 09:58:41
%S 1,1,1,1,1,1,2,2,1,1,2,2,2,1,1,4,4,3,2,1,1,5,4,4,3,2,1,1,7,7,6,5,3,2,
%T 1,1,10,9,8,6,5,3,2,1,1,13,13,11,10,7,5,3,2,1,1,17,16,15,12,10,7,5,3,
%U 2,1,1,24,24,21,18,14,11,7,5,3,2,1,1
%N Triangle read by rows: N_s(n,k) of spt-crank coefficients, n >= 1, k >= 0.
%C It appears this is the same as A195011 but without its right border (for this sequence see Garvan's slides, 2012).
%C It appears that reversed rows converge to A000041.
%H George E. Andrews, Freeman J. Dyson, and Robert C. Rhoades, <a href="https://doi.org/10.3390/math1030076">On the Distribution of the spt-Crank</a>, Mathematics 2013, 1, 76-88.
%H G. E. Andrews, F. G. Garvan, and J. Liang, <a href="https://georgeandrews1.github.io/pdf/287.pdf">Combinatorial interpretation of congruences for the spt-function</a>
%H F. G. Garvan, <a href="https://carma.newcastle.edu.au/meetings/alfcon/pdfs/Frank_Garvan-alfcon.pdf">The smallest parts partition function</a>, slides, 2012.
%e 1;
%e 1, 1;
%e 1, 1, 1;
%e 2, 2, 1, 1;
%e 2, 2, 2, 1, 1;
%e 4, 4, 3, 2, 1, 1;
%e 5, 4, 4, 3, 2, 1, 1;
%e 7, 7, 6, 5, 3, 2, 1, 1;
%e 10, 9, 8, 6, 5, 3, 2, 1, 1;
%e 13, 13, 11, 10, 7, 5, 3, 2, 1, 1;
%e 17, 16, 15, 12, 10, 7, 5, 3, 2, 1, 1;
%e 24, 24, 21, 18, 14, 11, 7, 5, 3, 2, 1, 1;
%Y Column 1 is A195012.
%Y Cf. A000041, A092269, A195011.
%K nonn,tabl
%O 1,7
%A _Omar E. Pol_, Jan 15 2013
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