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A155834 A triangle sequence of general recursive Sierpinski-Pascal minus general Narayana with adjusted n,m levels and zeros out:k=2; t(n,m)=Pascal(n,m,k-1)-Narayana(n-1,m-1,2*(k-1)).

%I A155834 #2 Mar 30 2012 17:34:33
%S A155834 1,1,6,16,6,22,127,127,22,64,701,1436,701,64,163,3117,11503,11503,
%T A155834 3117,163,382,12088,74122,131494,74122,12088,382,848,42890,413612,
%U A155834 1193930,1193930,413612,42890,848,1816,143562,2094588,9280734,14992440,9280734
%N A155834 A triangle sequence of general recursive Sierpinski-Pascal minus general Narayana with adjusted n,m levels and zeros out:k=2; t(n,m)=Pascal(n,m,k-1)-Narayana(n-1,m-1,2*(k-1)).
%C A155834 Row sums are;
%C A155834 2, 28, 298, 2966, 29566, 304678, 3302560, 38033840, 467861040, 6159690808,
%C A155834 86763791762,...
%C A155834 This level is the Eulerian number level:
%C A155834 only the odd Narayana levels correspond to the recursive Sierpinski-Pascal levels.
%F A155834 Pascal(n,m,k):
%F A155834 a(n,k,m)=(m*n - m*k + 1)*a(n - 1, k - 1, m) + (m*k - (m - 1))*a(n - 1, k, m);
%F A155834 Narayana(n,m,k):
%F A155834 y(n,m,k)=Product[Binomial[n + k, m + k]/Binomial[n - m + k, k], {k, 0, i}];
%F A155834 k=2;
%F A155834 t(n,m)=Pascal(n,m,k-1)-Narayana(n-1,m-1,2*(k-1)).
%e A155834 {1, 1},
%e A155834 {6, 16, 6},
%e A155834 {22, 127, 127, 22},
%e A155834 {64, 701, 1436, 701, 64},
%e A155834 {163, 3117, 11503, 11503, 3117, 163},
%e A155834 {382, 12088, 74122, 131494, 74122, 12088, 382},
%e A155834 {848, 42890, 413612, 1193930, 1193930, 413612, 42890, 848},
%e A155834 {1816, 143562, 2094588, 9280734, 14992440, 9280734, 2094588, 143562, 1816},
%e A155834 {3797, 462541, 9928140, 64761204, 158774838, 158774838, 64761204, 9928140, 462541, 3797},
%e A155834 {7814, 1453700, 44960878, 418557816, 1489425900, 2250878592, 1489425900, 418557816, 44960878, 1453700, 7814},
%e A155834 {15914, 4495909, 197226603, 2558716162, 12781854516, 27839586777, 27839586777, 12781854516, 2558716162, 197226603, 4495909, 15914}
%t A155834 Clear[A, a0, b0, n, k, m, t, i];
%t A155834 A[n_, 1, m_] := 1; A[n_, n_, m_] := 1;
%t A155834 A[n_, k_, m_] := (m*n - m*k + 1)*A[n - 1, k - 1, m] + (m*k - (m - 1))*A[n - 1, k, m];
%t A155834 t[n_, m_, i_] = Product[Binomial[n + k, m + k]/Binomial[n - m + k, k], {k, 0, i}];
%t A155834 m = 2; a = Table[A[n, k, m - 1] - t[n - 1, k - 1, (2*m - 2)], {n, 4, 14}, { k, 2, n - 1}];
%t A155834 Flatten[a]
%Y A155834 A001263, A056939.A056941, A142465, A142467
%K A155834 nonn,tabl,uned
%O A155834 4,3
%A A155834 _Roger L. Bagula_, Jan 28 2009