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 A307862 Coefficient of x^n in (1 + x - n*x^2)^n. 4
 1, 1, -3, -17, 49, 651, -1259, -38023, 26433, 2969299, 2225101, -289389891, -692529551, 33718183045, 143578976997, -4559187616649, -29119975483135, 699788001188403, 6188699469443869, -119828491083854707, -1404529670244379599, 22563726025297759345, 341997845736800473397 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also coefficient of x^n in the expansion of 1/sqrt(1 - 2*x + (1+4*n)*x^2). LINKS Seiichi Manyama, Table of n, a(n) for n = 0..500 FORMULA a(n) = Sum_{k=0..floor(n/2)} (-n)^k * binomial(n,k) * binomial(n-k,k) = Sum_{k=0..floor(n/2)} (-n)^k * binomial(n,2*k) * binomial(2*k,k). PROG (PARI) {a(n) = polcoef((1+x-n*x^2)^n, n)} (PARI) {a(n) = sum(k=0, n\2, (-n)^k*binomial(n, k)*binomial(n-k, k))} (PARI) {a(n) = sum(k=0, n\2, (-n)^k*binomial(n, 2*k)*binomial(2*k, k))} CROSSREFS Main diagonal of A307860. Cf. A002426, A187018, A307885. Sequence in context: A144640 A084069 A297514 * A132124 A011917 A018691 Adjacent sequences:  A307859 A307860 A307861 * A307863 A307865 A307866 KEYWORD sign AUTHOR Seiichi Manyama, May 02 2019 STATUS approved

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Last modified June 17 04:26 EDT 2019. Contains 324183 sequences. (Running on oeis4.)