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A152198 Triangle read by rows, A007318 rows repeated.

%I A152198 #33 Oct 20 2021 11:58:11
%S A152198 1,1,1,1,1,1,1,2,1,1,2,1,1,3,3,1,1,3,3,1,1,4,6,4,1,1,4,6,4,1,1,5,10,
%T A152198 10,5,1,1,5,10,10,5,1,1,6,15,20,15,6,1,1,6,15,20,15,6,1,1,7,21,35,35,
%U A152198 21,7,1,1,7,21,35,35,21,7,1,1,8,28,56,70,56,28,8,1,1,8,28,56,70,56,28,8,1
%N A152198 Triangle read by rows, A007318 rows repeated.
%C A152198 Eigensequence of the triangle = A051163: (1, 2, 5, 12, 30, 76,...)
%C A152198 Another version of A152815. - _Philippe Deléham_, Dec 13 2008
%C A152198 Row sums : A016116(n); Diagonal sums: A000931(n+5). - _Philippe Deléham_, Dec 13 2008
%C A152198 Triangle, with zeros omitted, given by (1, 0, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - _Philippe Deléham_, Jan 16 2012
%C A152198 Sums along rising diagonals are A134816. - _John Molokach_, Jul 09 2013
%F A152198 Triangle read by rows, Pascal's triangle rows repeated.
%F A152198 Equals inverse binomial transform of A133156 unsigned.
%F A152198 G.f. : (1+x)/(1-(1+y)*x^2). - _Philippe Deléham_, Jan 16 2012
%F A152198 Sum_{k, 0<=k<=n} T(n,k)*x^k = A057077(n), A019590(n+1), A000012(n), A016116(n), A108411(n), A074872(n+1) for x = -2, -1, 0, 1, 2, 4 respectively. - _Philippe Deléham_, Jan 16 2012
%F A152198 T(n,k) = A065941(n-k, n-2*k) = abs(A108299(n-k, n-2*k)). - _Johannes W. Meijer_, Sep 05 2013
%e A152198 The triangle starts
%e A152198 1;
%e A152198 1;
%e A152198 1, 1;
%e A152198 1, 1;
%e A152198 1, 2, 1;
%e A152198 1, 2, 1;
%e A152198 1, 3, 3, 1;
%e A152198 1, 3, 3, 1;
%e A152198 1, 4, 6, 4, 1;
%e A152198 1, 4, 6, 4, 1;
%e A152198 1, 5, 10, 10, 5, 1;
%e A152198 1, 5, 10, 10, 5, 1;
%e A152198 ...
%e A152198 Triangle (1,0,-1,0,0,...) DELTA (0,1,-1,0,0,...) begins:
%e A152198 1
%e A152198 1, 0
%e A152198 1, 1, 0
%e A152198 1, 1, 0, 0
%e A152198 1, 2, 1, 0, 0
%e A152198 1, 2, 1, 0, 0, 0
%e A152198 1, 3, 3, 1, 0, 0, 0
%e A152198 1, 3, 3, 1, 0, 0, 0, 0
%e A152198 1, 4, 6, 4, 1, 0, 0, 0, 0
%e A152198 1, 4, 6, 4, 1, 0, 0, 0, 0, 0
%e A152198 1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0...
%t A152198 t[n_, k_] := Binomial[ Floor[n/2], k]; Table[t[n, k], {n, 0, 17}, {k, 0, Floor[n/2]}] // Flatten (* _Jean-François Alcover_, Sep 13 2012 *)
%Y A152198 Cf. A007318, A133156, A051163.
%K A152198 nonn,tabf
%O A152198 0,8
%A A152198 _Gary W. Adamson_, Nov 28 2008
%E A152198 More terms from _Philippe Deléham_, Dec 14 2008