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 A300283 G.f. A(x) satisfies: [x^n] A( x/A(x)^(n+1) ) = 0 for n>1. 2
 1, 1, 3, 26, 390, 8379, 236243, 8336968, 357656013, 18278776900, 1095852254706, 76105128228036, 6057443479508005, 547449104446315498, 55722102673860207225, 6341532269895314369024, 801751668174625104196718, 111957760296735373861748037, 17178297525477106295505622856, 2882568247205689424775588032950, 526750240869807153027501303387666 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Paul D. Hanna, Table of n, a(n) for n = 0..200 EXAMPLE G.f.: A(x) = 1 + x + 3*x^2 + 26*x^3 + 390*x^4 + 8379*x^5 + 236243*x^6 + 8336968*x^7 + 357656013*x^8 + 18278776900*x^9 + ... The table of coefficients in A( x/A(x)^(n+1) ) begins: n=1: [1, 1, 2, 18, 282, 6290, 182795, 6610758, 289336014, ...]; n=2: [1, 1, 1, 11, 190, 4517, 137296, 5133692, 230534949, ...]; n=3: [1, 1, 0, 5, 113, 3030, 98861, 3875903, 180074370, ...]; n=4: [1, 1, -1, 0, 50, 1800, 66661, 2810026, 136890273, ...]; n=5: [1, 1, -2, -4, 0, 799, 39922, 1911092, 100025915, ...]; n=6: [1, 1, -3, -7, -38, 0, 17924, 1156423, 68624835, ...]; n=7: [1, 1, -4, -9, -65, -623, 0, 525528, 41924078, ...]; n=8: [1, 1, -5, -10, -82, -1095, -14465, 0, 19247621, ...]; n=9: [1, 1, -6, -10, -90, -1440, -26035, -436586, 0, ...]; n=10: [1, 1, -7, -9, -90, -1681, -35224, -798774, -16339863, 0, ...]; ... in which the main diagonal is all zeros after the initial terms. PROG (PARI) {a(n) = my(A=[1, 1]); for(i=2, n, A=concat(A, 0); A[#A] = -Vec(subst(Ser(A), x, x/Ser(A)^(#A)))[#A]); A[n+1]} for(n=0, 30, print1(a(n), ", ")) CROSSREFS Cf. A266489, A300732, A300733. Sequence in context: A262301 A317654 A143155 * A326431 A206403 A192554 Adjacent sequences: A300280 A300281 A300282 * A300284 A300285 A300286 KEYWORD nonn AUTHOR Paul D. Hanna, Mar 11 2018 STATUS approved

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Last modified November 30 15:21 EST 2022. Contains 358442 sequences. (Running on oeis4.)