A155834 - OEIS

%I #2 Mar 30 2012 17:34:33

%S 1,1,6,16,6,22,127,127,22,64,701,1436,701,64,163,3117,11503,11503,

%T 3117,163,382,12088,74122,131494,74122,12088,382,848,42890,413612,

%U 1193930,1193930,413612,42890,848,1816,143562,2094588,9280734,14992440,9280734

%N 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 Row sums are;

%C 2, 28, 298, 2966, 29566, 304678, 3302560, 38033840, 467861040, 6159690808,

%C 86763791762,...

%C This level is the Eulerian number level:

%C only the odd Narayana levels correspond to the recursive Sierpinski-Pascal levels.

%F Pascal(n,m,k):

%F 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 Narayana(n,m,k):

%F y(n,m,k)=Product[Binomial[n + k, m + k]/Binomial[n - m + k, k], {k, 0, i}];

%F k=2;

%F t(n,m)=Pascal(n,m,k-1)-Narayana(n-1,m-1,2*(k-1)).

%e {1, 1},

%e {6, 16, 6},

%e {22, 127, 127, 22},

%e {64, 701, 1436, 701, 64},

%e {163, 3117, 11503, 11503, 3117, 163},

%e {382, 12088, 74122, 131494, 74122, 12088, 382},

%e {848, 42890, 413612, 1193930, 1193930, 413612, 42890, 848},

%e {1816, 143562, 2094588, 9280734, 14992440, 9280734, 2094588, 143562, 1816},

%e {3797, 462541, 9928140, 64761204, 158774838, 158774838, 64761204, 9928140, 462541, 3797},

%e {7814, 1453700, 44960878, 418557816, 1489425900, 2250878592, 1489425900, 418557816, 44960878, 1453700, 7814},

%e {15914, 4495909, 197226603, 2558716162, 12781854516, 27839586777, 27839586777, 12781854516, 2558716162, 197226603, 4495909, 15914}

%t Clear[A, a0, b0, n, k, m, t, i];

%t A[n_, 1, m_] := 1; A[n_, n_, m_] := 1;

%t 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 t[n_, m_, i_] = Product[Binomial[n + k, m + k]/Binomial[n - m + k, k], {k, 0, i}];

%t 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 Flatten[a]

%Y A001263, A056939.A056941, A142465, A142467

%K nonn,tabl,uned

%O 4,3

%A _Roger L. Bagula_, Jan 28 2009