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

1,2

Links

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

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A325124 A231013 A231008 * A335365 A186386 A247589

Adjacent sequences: A092308 A092309 A092310 * A092312 A092313 A092314

Keyword

easy,nonn

Author

Vladeta Jovovic, Feb 16 2004

Extensions

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

Status

approved