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 A182059 Triangle, read by rows, given by (0, 2, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (2, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. 1
 1, 0, 2, 0, 4, 4, 0, 6, 12, 8, 0, 8, 24, 32, 16, 0, 10, 40, 80, 80, 32, 0, 12, 60, 160, 240, 192, 64, 0, 14, 84, 280, 560, 672, 448, 128, 0, 16, 112, 448, 1120, 1792, 1792, 1024, 256, 0, 18, 144, 672, 2016, 4032, 5376, 4608, 2304, 512 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Row sums are 3^n - 1 + 0^n. Triangle of coefficients in expansion of (1+2*x)^n - 1 + 0^n . LINKS FORMULA G.f.: (1-2*x+x^2+2*y*x^2)/(1-2*x-2*y*x+x^2+2*y*x^2). T(n,k) = 2*T(n-1,k) + 2*T(n-1,k-1) - T(n-2,k) - 2*T(n-2,k-1), T(0,0) = 1, T(1,0) = T(2,0) = 0, T(1,1) = 2, T(2,1) = T(2,2) = 4 and T(n,k) = 0 if k<0 or if k>n. T(n,k) = A206735(n,k)*2^k. T(n,k) = A013609(n,k) - A073424(n,k) . EXAMPLE Triangle begins : 1 0, 2 0, 4, 4 0, 6, 12, 8 0, 8, 24, 32, 16 0, 10, 40, 80, 80, 32 0, 12, 60, 160, 240, 192, 64 0, 14, 84, 280, 560, 672, 448, 128 0, 16, 112, 448, 1120, 1792, 1792, 1024, 256 0, 18, 144, 672, 2016, 4032, 5376, 4608, 2304, 512 0, 20, 180, 960, 3360, 8064, 13440, 15360, 11520, 5120, 1024 CROSSREFS Cf. A000079, A007318, A013609, A193789, A193790 Sequence in context: A307658 A265511 A081236 * A103328 A167312 A114122 Adjacent sequences:  A182056 A182057 A182058 * A182060 A182061 A182062 KEYWORD easy,nonn,tabl AUTHOR Philippe Deléham, Apr 09 2012 STATUS approved

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Last modified April 3 13:32 EDT 2020. Contains 333197 sequences. (Running on oeis4.)