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A182708
a(n) is the sum of the smallest parts of all partitions of n that do not contain 1 as a part.
4
0, 2, 3, 6, 7, 13, 14, 23, 27, 39, 45, 67, 75, 104, 125, 165, 194, 258, 302, 392, 467, 588, 700, 885, 1045, 1296, 1546, 1897, 2249, 2753, 3252, 3945, 4670, 5616, 6633, 7957, 9357, 11157, 13124, 15573, 18257, 21599, 25259, 29760, 34760, 40788, 47526, 55642, 64669, 75465, 87576, 101898, 117991, 136977, 158286
OFFSET
1,2
COMMENTS
In other words, sum of the smallest parts of all partitions of the head of the last section of the set of partitions of n.
Only one of the smallest parts is used in the sum.
LINKS
FORMULA
a(n) = A046746(n) - A000041(n-1).
a(n) ~ Pi * exp(Pi*sqrt(2*n/3)) / (6*sqrt(2)*n^(3/2)) * (1 + (11*Pi/(24*sqrt(6)) - 3*sqrt(3/2)/Pi)/sqrt(n)). - Vaclav Kotesovec, Jan 03 2019, extended Jul 06 2019
MATHEMATICA
Table[Total[{Min /@ IntegerPartitions[n, All, Range[2, n]]}, 2], {n, 55}] (* Robert Price, Aug 30 2020 *) (* Only suitable for n<100 *)
PROG
(PARI) my(N=66, z='z+O('z^N)); gf=sum(k=1, N, k * z^k / prod(j=k, N, 1-z^j ) ) - z/eta(z); concat([0], Vec(gf)) \\ Joerg Arndt, Aug 31 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Nov 28 2010
STATUS
approved