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A096652 Lower triangular matrix T, read by rows, such that the row sums of T^n form the (2n)-dimensional partition numbers.

%I A096652 #3 Mar 30 2012 18:36:40
%S A096652 1,0,1,0,2,1,0,3,2,1,0,5,5,2,1,0,7,7,7,2,1,0,11,16,9,9,2,1,0,15,15,31,
%T A096652 11,11,2,1,0,22,59,-4,54,13,13,2,1,0,30,-109,313,-72,87,15,15,2,1,0,
%U A096652 42,1314,-1922,1122,-225,132,17,17,2,1,0,56,-11804,19468,-9671,3087,-509,191,19,19,2,1,0,77,133957,-217176,110734,-32581
%N A096652 Lower triangular matrix T, read by rows, such that the row sums of T^n form the (2n)-dimensional partition numbers.
%C A096652 Row sums of T form A000219 (planar partitions); row sums of T^2 form A000334(4-D); row sums of T^3 form A000416(6-D).
%F A096652 Matrix square of triangle A096651.
%e A096652 Triangle T begins:
%e A096652 {1},
%e A096652 {0,1},
%e A096652 {0,2,1},
%e A096652 {0,3,2,1},
%e A096652 {0,5,5,2,1},
%e A096652 {0,7,7,7,2,1},
%e A096652 {0,11,16,9,9,2,1},
%e A096652 {0,15,15,31,11,11,2,1},
%e A096652 {0,22,59,-4,54,13,13,2,1},
%e A096652 {0,30,-109,313,-72,87,15,15,2,1},
%e A096652 {0,42,1314,-1922,1122,-225,132,17,17,2,1},
%e A096652 {0,56,-11804,19468,-9671,3087,-509,191,19,19,2,1},
%e A096652 {0,77,133957,-217176,110734,-32581,7137,-980,266,21,21,2,1},
%e A096652 {0,101,-1728760,2809257,-1426436,422732,-87714,14601,-1704,359,23,23,2,1},...
%e A096652 Row sums are: {1,1,3,6,13,24,48,86,160,282,500,859,...} (A000219).
%e A096652 T^2 begins:
%e A096652 {1},
%e A096652 {0,1},
%e A096652 {0,4,1},
%e A096652 {0,10,4,1},
%e A096652 {0,26,14,4,1},
%e A096652 {0,59,38,18,4,1},
%e A096652 {0,140,109,50,22,4,1},
%e A096652 {0,307,256,179,62,26,4,1},
%e A096652 {0,684,709,370,273,74,30,4,1},
%e A096652 {0,1464,1240,1683,438,395,86,34,4,1},...
%e A096652 with row sums: {1,1,5,15,45,120,326,835,2145,5345,...} (A000334).
%Y A096652 Cf. A096651, A000219, A000334, A000416.
%K A096652 sign,tabl
%O A096652 0,5
%A A096652 _Paul D. Hanna_, Jul 06 2004