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 A137156 Matrix inverse of triangle A137153(n,k) = C(2^k+n-k-1, n-k), read by rows. 6
 1, -1, 1, 1, -2, 1, -2, 5, -4, 1, 9, -24, 22, -8, 1, -88, 239, -228, 92, -16, 1, 1802, -4920, 4749, -1976, 376, -32, 1, -75598, 206727, -200240, 84086, -16432, 1520, -64, 1, 6421599, -17568408, 17034964, -7173240, 1413084, -133984, 6112, -128, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Unsigned column 0 = A001192, number of full sets of size n. LINKS FORMULA G.f. of column k: 1 = Sum_{n>=0} T(n+k,k)*x^n/(1-x)^(2^(n+k)). EXAMPLE Triangle begins: 1; -1, 1; 1, -2, 1; -2, 5, -4, 1; 9, -24, 22, -8, 1; -88, 239, -228, 92, -16, 1; 1802, -4920, 4749, -1976, 376, -32, 1; -75598, 206727, -200240, 84086, -16432, 1520, -64, 1; 6421599, -17568408, 17034964, -7173240, 1413084, -133984, 6112, -128, 1; ... PROG (PARI) /* As matrix inverse of A137153: */ {T(n, k) = local(M=matrix(n+1, n+1, r, c, if(r>=c, binomial(2^(c-1)+r-c-1, r-c)))); if(n

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Last modified January 25 21:23 EST 2021. Contains 340427 sequences. (Running on oeis4.)