A304631 - OEIS

%I #10 May 19 2018 04:31:31

%S 1,2,2,3,4,5,6,7,9,11,13,15,18,21,24,28,33,38,43,49,56,64,72,81,92,

%T 104,116,130,146,163,181,201,224,249,275,304,337,372,409,450,496,545,

%U 597,654,717,785,857,935,1022,1115,1213,1320,1437,1562,1695,1839,1996,2164,2342,2534

%N Expansion of (1/(1 - x))*Product_{k>=1} (1 + x^(2*k-1)).

%C Partial sums of A000700.

%H Vaclav Kotesovec, <a href="/A304631/b304631.txt">Table of n, a(n) for n = 0..2000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Self-ConjugatePartition.html">Self-Conjugate Partition</a>

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F G.f.: (1/(1 - x))*Product_{k>=1} 1/(1 + (-x)^k).

%F a(n) ~ exp(Pi*sqrt(n/6)) * 3^(1/4) / (Pi * 2^(1/4) * n^(1/4)). - _Vaclav Kotesovec_, May 19 2018

%t nmax = 59; CoefficientList[Series[1/(1 - x) Product[(1 + x^(2 k - 1)), {k, 1, nmax}], {x, 0, nmax}], x]

%t nmax = 59; CoefficientList[Series[1/(1 - x) Product[1/(1 + (-x)^k), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A000070, A000700, A036469, A218906, A304632.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, May 15 2018