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A121428 Rectangular table, read by antidiagonals, where row n is equal to column 2 of matrix power A121412^(n+1) for n>=0.

%I A121428 #3 Mar 30 2012 18:36:58
%S A121428 1,1,1,1,2,5,1,3,11,45,1,4,18,101,581,1,5,26,169,1305,9730,1,6,35,250,
%T A121428 2190,21745,199692,1,7,45,345,3255,36360,443329,4843125,1,8,56,455,
%U A121428 4520,53916,737051,10679494,135345925,1,9,68,581,6006,74781,1087583,17645187
%N A121428 Rectangular table, read by antidiagonals, where row n is equal to column 2 of matrix power A121412^(n+1) for n>=0.
%e A121428 Table of column 2 in matrix powers of triangle H=A121412 begins:
%e A121428 H^1: 1, 1, 5, 45, 581, 9730, 199692, 4843125, 135345925, ...
%e A121428 H^2: 1, 2, 11, 101, 1305, 21745, 443329, 10679494, 296547736, ...
%e A121428 H^3: 1, 3, 18, 169, 2190, 36360, 737051, 17645187, 487025244, ...
%e A121428 H^4: 1, 4, 26, 250, 3255, 53916, 1087583, 25889969, 710546530, ...
%e A121428 H^5: 1, 5, 35, 345, 4520, 74781, 1502270, 35578270, 971255050, ...
%e A121428 H^6: 1, 6, 45, 455, 6006, 99351, 1989113, 46890210, 1273698270, ...
%e A121428 H^7: 1, 7, 56, 581, 7735, 128051, 2556806, 60022670, 1622857887, ...
%e A121428 H^8: 1, 8, 68, 724, 9730, 161336, 3214774, 75190410, 2024181693, ...
%e A121428 H^9: 1, 9, 81, 885, 12015, 199692, 3973212, 92627235, 2483617140, ...
%e A121428 Rearrangement of the upper part of the table forms A121432, which is
%e A121428 the number of subpartitions of partition [0,0,0,1,1,1,1,2,2,2,2,2,..]:
%e A121428 1,1,1, 1,2,3,4, 5,11,18,26,35, 45,101,169,250,345,455, 581,1305,...
%o A121428 (PARI) {T(n,k)=local(H=Mat(1), B); for(m=1, k+3, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i, j]=1, B[i, j]=(H^i)[i-1, j]); )); H=B); return((H^(n+1))[k+3, 3])}
%Y A121428 Cf. A121429 (diagonal), A121431; rows: A121414, A121419, A121423; related tables: A121424, A121426; related triangles: A121412, A121416, A121420.
%K A121428 nonn,tabl
%O A121428 0,5
%A A121428 _Paul D. Hanna_, Aug 26 2006