A221140 Second-order spt function.

0, 1, 5, 15, 35, 75, 140, 259, 435, 735, 1155, 1841, 2765, 4200, 6125, 8975, 12731, 18179, 25235, 35180, 48055, 65681, 88299, 118895, 157690, 209230, 274510, 359779, 466970, 605740, 778860, 1000462, 1276044, 1624845, 2056355, 2598855, 3265851, 4097763, 5117350

Offset

1,3

Links

Jean-François Alcover, Table of n, a(n) for n = 1..60

F. G. Garvan, Higher-order spt functions, preprint.

F. G. Garvan, Higher-order spt functions, arXiv:1008.1207 [math.NT], 2010.

F. G. Garvan, Higher-order spt functions, Adv. Math. 228 (2011), no. 1, 241-265.

Mathematica

om[2, p_List] := Module[{pu, m, f}, pu = Union[p]; m = Length[pu]; f[j_] := Count[p, pu[[j]]]; Binomial[f[1] + 1, 3] + f[1] Sum[Binomial[f[j] + 1, 2], {j, 2, m}]];
spt[2, n_] := Sum[om[2, p], {p, IntegerPartitions[n]}];
Table[spt[2, n], {n, 1, 29}] (* Jean-François Alcover, Mar 30 2020 *)

Crossrefs

Cf. A092269, A221141, A221142, A221143, A221144.

Sequence in context: A368475 A261441 A213580 * A330911 A322048 A143695

Adjacent sequences: A221137 A221138 A221139 * A221141 A221142 A221143

Keyword

nonn

Author

N. J. A. Sloane, Jan 02 2013

Extensions

More terms from Jean-François Alcover, Mar 30 2020

Status

approved