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A097093 Number of partitions of n such that the least part occurs exactly five times. 4
0, 0, 0, 0, 1, 0, 1, 1, 2, 3, 4, 4, 8, 9, 14, 16, 23, 27, 39, 48, 62, 76, 100, 120, 159, 190, 241, 292, 367, 443, 552, 663, 816, 980, 1200, 1430, 1742, 2075, 2504, 2979, 3575, 4232, 5063, 5980, 7114, 8382, 9930, 11663, 13773, 16140, 18980, 22190, 26017 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

LINKS

Table of n, a(n) for n=1..53.

FORMULA

G.f.: Sum_{m>0} (x^(5*m) / Product_{i>m} (1-x^i)). More generally, g.f. for number of partitions of n such that the least part occurs exactly k times is Sum_{m>0} (x^(k*m) / Product_{i>m} (1-x^i)). Vladeta Jovovic

MATHEMATICA

f[n_] := Block[{p = IntegerPartitions[n], l = PartitionsP[n], c = 0, k = 1}, While[k < l + 1, q = PadLeft[ p[[k]], 6]; If[ q[[1]] != q[[6]] && q[[2]] == q[[6]], c++ ]; k++ ]; c]; Table[ f[n], {n, 54}]

CROSSREFS

Cf. A002865, A096373, A097091, A097092.

Sequence in context: A224038 A330147 A241037 * A056877 A267232 A269606

Adjacent sequences:  A097090 A097091 A097092 * A097094 A097095 A097096

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Jul 24 2004

STATUS

approved

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Last modified April 18 22:45 EDT 2021. Contains 343098 sequences. (Running on oeis4.)