cp's OEIS Frontend

A211183 Triangle T(n,k), 0<=k<=n, read by rows, given by (0, 1, 1, 3, 3, 6, 6, 10, 10, 15, ...) DELTA (1, 0, 2, 0, 3, 0, 4, 0, 5, ...) where DELTA is the operator defined in A084938.

%I A211183 #18 Jul 19 2016 11:32:18
%S A211183 1,0,1,0,1,1,0,2,4,1,0,7,19,11,1,0,38,123,107,26,1,0,295,1076,1195,
%T A211183 474,57,1,0,3098,12350,16198,8668,1836,120,1,0,42271,180729,268015,
%U A211183 176091,52831,6549,247,1,0,726734,3290353,5369639,4105015,1564817,287473,22145
%N A211183 Triangle T(n,k), 0<=k<=n, read by rows, given by (0, 1, 1, 3, 3, 6, 6, 10, 10, 15, ...) DELTA (1, 0, 2, 0, 3, 0, 4, 0, 5, ...) where DELTA is the operator defined in A084938.
%H A211183 Paul D. Hanna, <a href="/A211183/b211183.txt">Rows n = 0..31, flattened.</a>
%F A211183 Sum_{k, 0<=k<=n}T(n,k)*x^(n-k) = A000012(n), A000366(n+1), A110501(n+1), A211194(n), A221972(n) for x = 0, 1, 2, 3, 4 respectively.
%F A211183 T(n,n-1) = A000295(n).
%F A211183 T(n,1) = A000366(n).
%F A211183 G.f.: A(x,y) = Sum_{n>=0} n! * x^n * Product_{k=1..n} (y + (k-1)/2) / (1 + (k*y + k*(k-1)/2)*x). - _Paul D. Hanna_, Feb 03 2013
%e A211183 Triangle begins :
%e A211183 1;
%e A211183 0, 1;
%e A211183 0, 1, 1;
%e A211183 0, 2, 4, 1;
%e A211183 0, 7, 19, 11, 1;
%e A211183 0, 38, 123, 107, 26, 1;
%e A211183 0, 295, 1076, 1195, 474, 57, 1;
%e A211183 0, 3098, 12350, 16198, 8668, 1836, 120, 1;
%e A211183 0, 42271, 180729, 268015, 176091, 52831, 6549, 247, 1;
%e A211183 0, 726734, 3290353, 5369639, 4105015, 1564817, 287473, 22145, 502, 1; ...
%o A211183 (PARI) T(n,k)=polcoeff(polcoeff(sum(m=0, n, m!*x^m*prod(k=1, m, (y + (k-1)/2)/(1+(k*y+k*(k-1)/2)*x+x*O(x^n)))), n,x),k,y)
%o A211183 for(n=0,12,for(k=0,n,print1(T(n,k),", "));print()) \\ _Paul D. Hanna_, Feb 03 2013
%Y A211183 Cf. A000366, A110501, A211194, A221972.
%K A211183 nonn,tabl
%O A211183 0,8
%A A211183 _Philippe Deléham_, Feb 02 2013