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 A102916 Triangle, read by rows, where the antidiagonals are formed by interleaving the rows of triangle A102098 with the rows of its matrix square (A102920). 4
 1, 1, 2, 1, 4, 3, 3, 8, 9, 4, 7, 40, 27, 16, 5, 36, 152, 189, 64, 25, 6, 139, 1128, 999, 576, 125, 36, 7, 1036, 6200, 9720, 3904, 1375, 216, 49, 8, 5711, 61120, 69687, 47040, 11375, 2808, 343, 64, 9, 56355, 442552, 857466, 416704, 163500, 27432, 5145, 512 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Column 0 is A102917, the interleaving of A082162 with A102921. Under matrix cube, triangle A102098 shifts each column up 1 row. LINKS FORMULA G.f. for column k: T(k, k) = k+1 = Sum_{n>=0} T(n+k, k)*x^n*Product_{j=k..[n/2+k]} (1-(j+1)*x). EXAMPLE Rows begin: [1], [1,2], [1,4,3], [3,8,9,4], [7,40,27,16,5], [36,152,189,64,25,6], [139,1128,999,576,125,36,7], [1036,6200,9720,3904,1375,216,49,8], [5711,61120,69687,47040,11375,2808,343,64,9],... The antidiagonals are formed by interleaving the rows of triangle A102098: [1], [1,2], [7,8,3], [139,152,27,4],... with the rows of the matrix square of A102098, which is triangle A102920: [1], [3,4], [36,40,9], [1036,1128,189,16],... G.f. for Column 0 (A102917): 1 = 1*(1-x) + 1*x*(1-x) + 1*x^2*(1-x)(1-2x) + 3*x^3*(1-x)(1-2x) + 7*x^4*(1-x)(1-2x)(1-3x) + 36*x^5*(1-x)(1-2x)(1-3x) +... + A082162(n)*x^(2n)*(1-x)(1-2x)*..*(1-(n+1)x) + A102921(n)*x^(2n+1)*(1-x)(1-2x)*..*(1-(n+1)x) + ... G.f. for Column 1 (A102918): 2 = 2*(1-2x) + 4*x*(1-2x) + 8*x^2*(1-2x)(1-3x) + 40*x^3*(1-2x)(1-3x) + 152*x^4*(1-2x)(1-3x)(1-4x) + 1128*x^5*(1-2x)(1-3x)(1-4x) +... + T(2n+1,1)*x^(2n)*(1-2x)(1-3x)*..*(1-(n+2)x) + T(2n+2,1)*x^(2n+1)*(1-2x)(1-3x)*..*(1-(n+2)x) + ... PROG (PARI) {T(n, k)=if(n

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)