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 A134530 Matrix log of triangle A111636, where A111636(n,k) = (2^k)^(n-k)*C(n,k) for n>=k>=0. 2
 0, 1, 0, -1, 4, 0, 5, -12, 12, 0, -79, 160, -96, 32, 0, 3377, -6320, 3200, -640, 80, 0, -362431, 648384, -303360, 51200, -3840, 192, 0, 93473345, -162369088, 72619008, -11325440, 716800, -21504, 448, 0, -56272471039, 95716705280, -41566486528, 6196822016, -362414080, 9175040, -114688, 1024, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS FORMULA T(n,k) = A134531(n-k)*(2^k)^(n-k)*C(n,k), where A134531 is column 0 and satisfies: G.f.: Sum_{n>=0} A134531(n)*x^n/[n!*2^(n*(n-1)/2)] = log(Sum_{n>=0}x^n/[n!*2^(n*(n-1)/2)]). EXAMPLE Triangle begins: 0, 1, 0; -1, 4, 0; 5, -12, 12, 0; -79, 160, -96, 32, 0; 3377, -6320, 3200, -640, 80, 0; -362431, 648384, -303360, 51200, -3840, 192, 0; 93473345, -162369088, 72619008, -11325440, 716800, -21504, 448, 0; ... Matrix exponentiation yields triangle A111636, which begins: 1; 1, 1; 1, 4, 1; 1, 12, 12, 1; 1, 32, 96, 32, 1; 1, 80, 640, 640, 80, 1; ... PROG (PARI) {T(n, k)=local(M=matrix(n+1, n+1, r, c, if(r>=c, 2^((c-1)*(r-c))*binomial(r-1, c-1))), L); L=sum(i=1, #M, -(M^0-M)^i/i); L[n+1, k+1]} CROSSREFS Cf. A134531 (column 0); related triangles: A111636, A117401; A011266. Sequence in context: A064520 A267313 A108174 * A184365 A126813 A056141 Adjacent sequences:  A134527 A134528 A134529 * A134531 A134532 A134533 KEYWORD sign,tabl AUTHOR Paul D. Hanna, Oct 30 2007 STATUS approved

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Last modified May 26 19:30 EDT 2019. Contains 323597 sequences. (Running on oeis4.)