cp's OEIS Frontend

A358829 Number of twice-partitions of n with no (1)'s.

%I A358829 #5 Dec 03 2022 13:53:48
%S A358829 1,0,2,3,9,13,38,56,144,237,524,886,1961,3225,6700,11702,23007,39787,
%T A358829 77647,133707,254896,442736,820703,1427446,2630008,4535330,8224819,
%U A358829 14250148,25513615,43981753,78252954,134323368,236900355,406174046,709886932,1213934012
%N A358829 Number of twice-partitions of n with no (1)'s.
%C A358829 A twice-partition of n is a sequence of integer partitions, one of each part of an integer partition of n.
%F A358829 G.f.: Product_{k>=2} 1/(1-A000041(k)*x^k).
%e A358829 The a(2) = 2 through a(5) = 13 twice-partitions:
%e A358829   (2)   (3)    (4)       (5)
%e A358829   (11)  (21)   (22)      (32)
%e A358829         (111)  (31)      (41)
%e A358829                (211)     (221)
%e A358829                (1111)    (311)
%e A358829                (2)(2)    (2111)
%e A358829                (11)(2)   (3)(2)
%e A358829                (2)(11)   (11111)
%e A358829                (11)(11)  (21)(2)
%e A358829                          (3)(11)
%e A358829                          (111)(2)
%e A358829                          (21)(11)
%e A358829                          (111)(11)
%t A358829 twiptn[n_]:=Join@@Table[Tuples[IntegerPartitions/@ptn],{ptn,IntegerPartitions[n]}];
%t A358829 Table[Length[Select[twiptn[n],FreeQ[Total/@#,1]&]],{n,0,10}]
%Y A358829 The version for multiset partitions of integer partitions is A317911.
%Y A358829 Forbidding all singletons gives A358828.
%Y A358829 A002865 counts partitions with no 1's.
%Y A358829 A063834 counts twice-partitions, strict A296122, row-sums of A321449.
%Y A358829 Cf. A000009, A000041, A000219, A001970, A072233, A304966, A358824.
%K A358829 nonn
%O A358829 0,3
%A A358829 _Gus Wiseman_, Dec 03 2022