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 A318108 a(n) = Sum_{k=0..n} (3*n-2*k)!/((n-k)!^3*k!)*(-3)^k, n >= 0. 2
 1, 3, 27, 303, 3771, 49653, 677979, 9496791, 135572859, 1963940073, 28783474677, 425872190241, 6350923156059, 95341185353781, 1439433069482547, 21839152342265703, 332769145298428539, 5089688869615075521, 78108038975852093889, 1202268428203687094493, 18555675891246972931221 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Diagonal of rational function 1/(1 - (x + y + z - 3*x*y*z)). LINKS Seiichi Manyama, Table of n, a(n) for n = 0..829 (terms 0..100 from Gheorghe Coserea) FORMULA G.f. y=A(x) satisfies: 0 = x*(6*x - 1)*(27*x^3 + 27*x^2 - 18*x + 1)*y'' + (486*x^4 + 216*x^3 - 189*x^2 + 36*x - 1)*y' + 3*(3*x + 1)*(18*x^2 - 6*x + 1)*y. Recurrence: n^2*(3*n - 4)*a(n) = 3*(3*n - 2)*(6*n^2 - 10*n + 3)*a(n-1) - 9*(9*n^3 - 30*n^2 + 29*n - 6)*a(n-2) - 27*(n-2)^2*(3*n - 1)*a(n-3). - Vaclav Kotesovec, Mar 01 2019 EXAMPLE A(x) = 1 + 3*x + 27*x^2 + 303*x^3 + 3771*x^4 + 49653*x^5 + 677979*x^6 + ... MATHEMATICA Table[Sum[(3n-2k)!/(((n-k)!)^3 k!) (-3)^k, {k, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Mar 01 2019 *) PROG (PARI) a(n) = sum(k=0, n, (3*n-2*k)!/((n-k)!^3*k!)*(-3)^k); vector(21, n, a(n-1)) CROSSREFS Cf. A318107. Sequence in context: A214363 A204821 A200903 * A290576 A291315 A078532 Adjacent sequences:  A318105 A318106 A318107 * A318109 A318110 A318111 KEYWORD nonn AUTHOR Gheorghe Coserea, Sep 20 2018 STATUS approved

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Last modified September 21 09:52 EDT 2021. Contains 347597 sequences. (Running on oeis4.)