cp's OEIS Frontend

A358825 Number of ways to choose a sequence of integer partitions, one of each part of an integer partition of n into odd parts.

%I A358825 #7 Dec 04 2022 08:33:31
%S A358825 1,1,1,4,4,11,20,35,56,113,207,326,602,985,1777,3124,5115,8523,15011,
%T A358825 24519,41571,71096,115650,191940,320651,530167,865781,1442059,2358158,
%U A358825 3833007,6325067,10243259,16603455,27151086,43734197,71032191,115091799,184492464
%N A358825 Number of ways to choose a sequence of integer partitions, one of each part of an integer partition of n into odd parts.
%F A358825 G.f.: Product_{k odd} 1/(1-A000041(k)*x^k).
%e A358825 The a(1) = 1 through a(5) = 11 twice-partitions:
%e A358825   (1)  (1)(1)  (3)        (3)(1)        (5)
%e A358825                (21)       (21)(1)       (32)
%e A358825                (111)      (111)(1)      (41)
%e A358825                (1)(1)(1)  (1)(1)(1)(1)  (221)
%e A358825                                         (311)
%e A358825                                         (2111)
%e A358825                                         (11111)
%e A358825                                         (3)(1)(1)
%e A358825                                         (21)(1)(1)
%e A358825                                         (111)(1)(1)
%e A358825                                         (1)(1)(1)(1)(1)
%t A358825 twiptn[n_]:=Join@@Table[Tuples[IntegerPartitions/@ptn],{ptn,IntegerPartitions[n]}];
%t A358825 Table[Length[Select[twiptn[n],OddQ[Times@@Total/@#]&]],{n,0,10}]
%Y A358825 For odd parts instead of sums we have A270995.
%Y A358825 For distinct instead of odd sums we have A271619.
%Y A358825 Requiring odd length, odd lengths, and odd parts gives A279374 aerated.
%Y A358825 For odd lengths instead of sums we have A358334.
%Y A358825 The odd-length case is A358826.
%Y A358825 A000009 counts partitions into odd parts.
%Y A358825 A027193 counts partitions of odd length.
%Y A358825 A063834 counts twice-partitions, strict A296122, row-sums of A321449.
%Y A358825 A078408 counts odd-length partitions into odd parts.
%Y A358825 A300301 aerated counts twice-partitions with odd sums and parts.
%Y A358825 Cf. A000041, A001970, A072233, A279785, A356932, A358824.
%K A358825 nonn
%O A358825 0,4
%A A358825 _Gus Wiseman_, Dec 03 2022