%I A145515
%S A145515 1,1,1,1,1,1,1,2,1,1,1,2,4,1,1,1,2,5,10,1,1,1,2,6,23,36,1,1,1,2,7,46,
%T A145515 239,202,1,1,1,2,8,82,1086,5828,1828,1,1,1,2,9,134,3707,79326,342383,
%U A145515 27338,1,1,1,2,10,205,10340,642457,18583582,50110484,692004,1,1,1,2,11
%N A145515 Square array A(n,k), n>=0, k>=0, read by antidiagonals: A(n,k) is the 
               number of partitions of k^n into powers of k.
%H A145515 Alois P. Heinz, <a href="b145515.txt">Table of n, a(n) for n = 0..860</
               a>
%F A145515 See program.
%e A145515 A(2,3) = 5, because there are 5 partitions of 3^2=9 into powers of 3: 
               1+1+1+1+1+1+1+1+1, 1+1+1+1+1+1+3, 1+1+1+3+3, 3+3+3, 9.
%e A145515 Square array A(n,k) begins:
%e A145515 1 1 1 1 1 1 ...
%e A145515 1 1 2 2 2 2 ...
%e A145515 1 1 4 5 6 7 ...
%e A145515 1 1 10 23 46 82 ...
%e A145515 1 1 36 239 1086 3707 ...
%e A145515 1 1 202 5828 79326 642457
%p A145515 g:= proc(b,n,k) option remember; local t; if b<0 then 0 elif b=0 or n=0 
               or k<=1 then 1 elif b>=n then add (g(b-t, n, k) *binomial (n+1, t) 
               *(-1)^(t+1), t=1..n+1); else g(b-1, n, k) +g(b*k, n-1, k) fi end: 
               A:= (n,k)-> g(1,n,k): seq (seq (A(n,d-n), n=0..d), d=0..13);
%Y A145515 Columns 0+1, 2-10 give: A000012, A002577, A078125, A078537, A111822, 
               A111827, A111832, A111837, A145512, A145513. Diagonal gives: A145514. 
               Cf. A007318.
%Y A145515 Sequence in context: A129176 A134132 A030424 this_sequence A026519 A025177 
               A026148
%Y A145515 Adjacent sequences: A145512 A145513 A145514 this_sequence A145516 A145517 
               A145518
%K A145515 nonn,tabl
%O A145515 0,8
%A A145515 Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 11 2008