%I #23 Aug 31 2020 03:52:15

%S 0,2,3,6,7,13,14,23,27,39,45,67,75,104,125,165,194,258,302,392,467,

%T 588,700,885,1045,1296,1546,1897,2249,2753,3252,3945,4670,5616,6633,

%U 7957,9357,11157,13124,15573,18257,21599,25259,29760,34760,40788,47526,55642,64669,75465,87576,101898,117991,136977,158286

%N a(n) is the sum of the smallest parts of all partitions of n that do not contain 1 as a part.

%C 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.

%C Only one of the smallest parts is used in the sum.

%H Vaclav Kotesovec, <a href="/A182708/b182708.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A046746(n) - A000041(n-1).

%F 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

%t Table[Total[{Min /@ IntegerPartitions[n, All, Range[2, n]]}, 2], {n, 55}] (* _Robert Price_, Aug 30 2020 *) (* Only suitable for n<100 *)

%o (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

%Y Cf. A000041, A046746, A135010, A138121, A182707, A182709.

%K nonn,easy

%O 1,2

%A _Omar E. Pol_, Nov 28 2010