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 A108624 G.f. satisfies x = (A(x)+(A(x))^2)/(1-A(x)-(A(x))^2). 3
 1, 0, -1, 1, 1, -4, 3, 8, -23, 10, 67, -153, 9, 586, -1081, -439, 5249, -7734, -7941, 47501, -53791, -105314, 430119, -343044, -1249799, 3866556, -1730017, -13996097, 34243897, -1947204, -150962373, 296101864, 121857185 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Row sums of triangle A202327. - Peter Luschny, Apr 26 2017 LINKS FORMULA a(n) = sum(k=1..n, (k*sum(j=0..n, binomial(j,-n-k+2*j)*(-1)^(j-k)*binomial(n,j))))/n. - Vladimir Kruchinin, May 19 2012 MATHEMATICA a[n_] := Sum[k Sum[Binomial[j, -n - k + 2j] (-1)^(j - k) Binomial[n, j], {j, 0, n}], {k, 1, n}]/n; Array[a, 33] (* Jean-François Alcover, Jun 13 2019, after Vladimir Kruchinin *) PROG (Julia) function A108624_list(len::Int)     len <= 0 && return BigInt[]     T = zeros(BigInt, len, len); T[1, 1] = 1     S = Array(BigInt, len); S[1] = 1     for n in 2:len         T[n, n] = 1         for k in 1:n-1             T[n, k] = (k > 1 ? T[n-1, k-1] : 0) - T[n-1, k] - T[n-1, k+1]         end         S[n] = sum(T[n, k] for k in 1:n)     end S end println(A108624_list(33)) # Peter Luschny, Apr 27 2017 CROSSREFS Cf. A039980, A202327. Except for signs, same as A108623. Sequence in context: A137503 A320263 A215330 * A108623 A248248 A159550 Adjacent sequences:  A108621 A108622 A108623 * A108625 A108626 A108627 KEYWORD sign AUTHOR Christian G. Bower, Jun 12 2005 STATUS approved

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Last modified May 5 23:41 EDT 2021. Contains 343579 sequences. (Running on oeis4.)