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A132825 Triangle read by rows: zeros except for right border which are the partition numbers A000041.

%I A132825 #14 Mar 06 2022 08:36:52
%S A132825 1,0,2,0,0,3,0,0,0,5,0,0,0,0,7,0,0,0,0,0,11,0,0,0,0,0,0,15,0,0,0,0,0,
%T A132825 0,0,22,0,0,0,0,0,0,0,0,30,0,0,0,0,0,0,0,0,0,42,0,0,0,0,0,0,0,0,0,0,
%U A132825 56,0,0,0,0,0,0,0,0,0,0,0,77,0,0,0,0,0,0,0,0,0,0,0,0,101
%N A132825 Triangle read by rows: zeros except for right border which are the partition numbers A000041.
%C A132825 Row sums = partition numbers, A000041 starting with A000041(1).
%C A132825 A132825 * [1, 2, 3, ...] = A066186.
%H A132825 Robert Price, <a href="/A132825/b132825.txt">Table of n, a(n) for n = 1..1275, 50 rows.</a>
%F A132825 Infinite lower triangular matrix, partition numbers (A000041, starting 1, 2, 3, 5, 7, 11, ...) in the main diagonal and the rest zeros.
%e A132825 First few rows of the triangle:
%e A132825   1;
%e A132825   0, 2;
%e A132825   0, 0, 3;
%e A132825   0, 0, 0, 5;
%e A132825   0, 0, 0, 0, 7;
%e A132825   0, 0, 0, 0, 0, 11;
%e A132825   ...
%t A132825 Table[Join[ConstantArray[0, n - 1], {PartitionsP[n]}], {n, 13}] // Flatten (* _Robert Price_, May 19 2020 *)
%t A132825 Table[Join[PadRight[{},n-1,0],{PartitionsP[n]}],{n,20}]//Flatten (* _Harvey P. Dale_, Sep 14 2021 *)
%Y A132825 Cf. A000041, A066186.
%K A132825 nonn,tabl
%O A132825 1,3
%A A132825 _Gary W. Adamson_, Sep 02 2007