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 A172400 G.f.: 1/(1-x) = (1-x*y) * Sum_{k>=0} Sum_{n>=k} T(n,k)*x^n*y^k/(1+x)^(2^n-2^k). 3
 1, 1, 1, 2, 1, 1, 6, 3, 1, 1, 32, 16, 5, 1, 1, 332, 166, 51, 9, 1, 1, 6928, 3464, 1059, 181, 17, 1, 1, 292334, 146167, 44620, 7557, 681, 33, 1, 1, 24875760, 12437880, 3795202, 641035, 57097, 2641, 65, 1, 1, 4254812880, 2127406440, 649054326, 109540639 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS FORMULA Unsigned column 0 of matrix inverse forms A001192, which is the number of full sets of size n. EXAMPLE Triangle begins: 1; 1, 1; 2, 1, 1; 6, 3, 1, 1; 32, 16, 5, 1, 1; 332, 166, 51, 9, 1, 1; 6928, 3464, 1059, 181, 17, 1, 1; 292334, 146167, 44620, 7557, 681, 33, 1, 1; 24875760, 12437880, 3795202, 641035, 57097, 2641, 65, 1, 1; 4254812880, 2127406440, 649054326, 109540639, 9723237, 443921, 10401, 129, 1, 1; ... Matrix inverse of this triangle begins: 1; -1,1; -1,-1,1; -2,-2,-1,1; -9,-9,-4,-1,1; -88,-88,-38,-8,-1,1; -1802,-1802,-772,-156,-16,-1,1; -75598,-75598,-32313,-6456,-632,-32,-1,1; ... in which unsigned column 0 = A001192, number of full sets of size n. PROG (PARI) {T(n, k)=if(n==k, 1, polcoeff(-(1-x)*sum(m=0, n-k-1, T(m+k, k)*x^m/(1+x +x*O(x^n))^(2^(m+k)-2^k)), n-k))} (PARI) {T(n, k)=local(M, N); M=matrix(n+1, n+1, r, c, if(r>=c, polcoeff(1/(1-x+O(x^(r-c+1)))^1*(1+x)^(2^(r-1)-2^(c-1)), r-c))); N=matrix(n+1, n+1, r, c, if(r>=c, polcoeff(1/(1-x+O(x^(r-c+1)))^2*(1+x)^(2^(r-1)-2^(c-1)), r-c))); (M^-1*N)[n+1, k+1]} CROSSREFS Cf. A001192, columns: A172401, A172402, A172403. Sequence in context: A213936 A142589 A284308 * A226691 A158389 A186287 Adjacent sequences:  A172397 A172398 A172399 * A172401 A172402 A172403 KEYWORD nonn,tabl AUTHOR Paul D. Hanna, Feb 01 2010 STATUS approved

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Last modified February 27 07:04 EST 2020. Contains 332299 sequences. (Running on oeis4.)