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 A089949 Triangle T(n,k), read by rows, given by : [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, ...] DELTA [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, ...] where DELTA is the operator defined in A084938. 10
 1, 0, 1, 0, 1, 2, 0, 1, 6, 6, 0, 1, 12, 34, 24, 0, 1, 20, 110, 210, 120, 0, 1, 30, 270, 974, 1452, 720, 0, 1, 42, 560, 3248, 8946, 11256, 5040, 0, 1, 56, 1036, 8792, 38338, 87504, 97296, 40320, 0, 1, 72, 1764, 20580, 129834, 463050, 920184, 930960, 362880 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Diagonals : A000007 A000012 A002378; A000142 . Row sums : A003319. Row reverse appears to be A111184. - Peter Bala, Feb 17 2017 LINKS Alois P. Heinz, Rows n = 0..140, flattened FORMULA Sum_{k = 0...n} x^(n-k)*T(n, k) = A111528(x, n); see A000142, A003319, A111529, A111530, A111531, A111532, A111533 for x = 0, 1, 2, 3, 4, 5, 6 . - Philippe Deléham, Aug 09 2005 Sum_{k, 0<=k<=n} T(n, k)*3^k = A107716(n) . - Philippe Deléham, Aug 15 2005 Sum_{k, 0<=k<=n} T(n, k)*2^k = A000698(n+1) . - Philippe Deléham, Aug 15 2005 G.f.: A(x, y) = (1/x)*(1 - 1/(1 + Sum_{n>=1} [Prod_{k=0..n-1}(1+k*y)]*x^n )). - Paul D. Hanna, Aug 16 2005 EXAMPLE Triangle begins: 1; 0,1; 0,1,2; 0,1,6,6; 0,1,12,34,24; 0,1,20,110,210,120; 0,1,30,270,974,1452,720; ... MATHEMATICA m = 10; gf = (1/x)*(1-1/(1+Sum[Product[(1+k*y), {k, 0, n-1}]*x^n, {n, 1, m}])); CoefficientList[#, y]& /@ CoefficientList[gf + O[x]^m, x] // Flatten (* Jean-François Alcover, May 11 2019 *) PROG (PARI) T(n, k)=if(n

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Last modified October 23 22:52 EDT 2019. Contains 328378 sequences. (Running on oeis4.)