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%I #10 Sep 08 2013 13:30:13
%S 1,0,1,0,1,4,0,4,23,34,0,34,249,606,496,0,496,4354,14181,20434,11056,
%T 0,11056,112238,450097,894838,885032,349504,0,349504,4008024,18911670,
%U 47136095,65613780,48468804,14873104
%N Triangle T(n,k) read by rows given by [0, 1, 3, 6, 10, 15, 21, ...] DELTA [1, 3, 6, 10, 15, 21, 28,...] where DELTA is the operator defined in A084938.
%F Sum_{k, 0<=k<=n}T(n,k)*x^(n-k)=A000012(n), A011782(n), A001147(n), A002105(n+1), A000364(n), A126151(n), A126156(n) for n = -3,-2,-1,0,1,2,3 respectively .
%e Triangle begins:
%e 1;
%e 0, 1;
%e 0, 1, 4;
%e 0, 4, 23, 34;
%e 0, 34, 249, 606, 496;
%e 0, 496, 4354, 14181, 20434, 11056;
%e 0, 11056, 112238, 450097, 894838, 885032, 349504;
%e 0, 349504, 4008024, 18911670, 47136095, 65613780, 48468804, 14873104 ;...
%Y Diagonals give A002105: [1, 1, 4, 34, 496, ...] Row sums give A000364 : [1, 1, 5, 61, 1385, ...] Euler numbers.
%Y Cf. A000217 A000384 A002105 A084938.
%K easy,nonn,tabl
%O 0,6
%A _Philippe Deléham_, Sep 30 2003, Jul 17 2007
%E Corrected and edited. - _Philippe Deléham_, Nov 24 2008
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