A220163 Triangle read by rows: N_s(n,k) of spt-crank coefficients, n >= 1, k >= 0.

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, 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, 2, 1, 1, 24, 24, 21, 18, 14, 11, 7, 5, 3, 2, 1, 1

Offset: 1

Author

Omar E. Pol, Jan 15 2013

Keywords

• nonn
• tabl

Comments

It appears this is the same as A195011 but without its right border (for this sequence see Garvan's slides, 2012).

It appears that reversed rows converge to A000041.

Examples

			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,  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,  2,  1,  1;
24, 24, 21, 18, 14, 11,  7,  5,  3,  2,  1,  1;
		

Links

• George E. Andrews, Freeman J. Dyson, and Robert C. Rhoades, On the Distribution of the spt-Crank, Mathematics 2013, 1, 76-88.
• G. E. Andrews, F. G. Garvan, and J. Liang, Combinatorial interpretation of congruences for the spt-function
• F. G. Garvan, The smallest parts partition function, slides, 2012.

Crossrefs

Column 1 is A195012.

Cf. A000041, A092269, A195011.