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A221140 Second-order spt function. 7
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 (list; graph; refs; listen; history; text; internal format)
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: A270784 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

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Last modified June 27 13:59 EDT 2022. Contains 354896 sequences. (Running on oeis4.)