A092311 Total number of largest parts in all partitions of n into odd parts.

1, 2, 4, 5, 7, 10, 12, 14, 19, 23, 26, 33, 38, 44, 56, 63, 71, 88, 99, 114, 138, 155, 176, 208, 237, 269, 314, 357, 402, 468, 529, 594, 686, 772, 873, 999, 1119, 1260, 1431, 1608, 1804, 2039, 2284, 2554, 2884, 3219, 3590, 4032, 4493, 5011, 5603, 6231, 6928

Offset: 1

Author

Vladeta Jovovic, Feb 16 2004

Keywords

• easy
• nonn

Examples

			Partitions of 6 into odd parts are: [1,1,1,1,1,1], [1,1,1,3], [3,3], [1,5]; thus a(6)=6+1+2+1=10.
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..2500

Crossrefs

Cf. A092314, A092322, A092269, A092309, A092321, A092313, A092310, A092268.

Programs

Mathematica

nmax = 50; Rest[CoefficientList[Series[Sum[(x^(2*n - 1)/(1 - x^(2*n - 1))) / Product[(1 - x^(2*k - 1)), {k, 1, n}], {n, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Jul 06 2019 *)
lpp[k_]:=Module[{c=Max[k]},Count[k,c]]; Table[Total[lpp/@Select[IntegerPartitions[ n],AllTrue[ #,OddQ]&]],{n, 60}] (* Harvey P. Dale, Apr 24 2023 *)

Formula

G.f.: Sum((x^(2*n-1)/(1-x^(2*n-1)))/Product((1-x^(2*k-1)), k=1..n), n=1..infinity).

a(n) ~ exp(Pi*sqrt(n/3)) / (4 * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 07 2019

Extensions

More terms from Pab Ter (pabrlos(AT)yahoo.com), May 25 2004