A300283 - OEIS

%I #6 Mar 11 2018 20:19:06

%S 1,1,3,26,390,8379,236243,8336968,357656013,18278776900,1095852254706,

%T 76105128228036,6057443479508005,547449104446315498,

%U 55722102673860207225,6341532269895314369024,801751668174625104196718,111957760296735373861748037,17178297525477106295505622856,2882568247205689424775588032950,526750240869807153027501303387666

%N G.f. A(x) satisfies: [x^n] A( x/A(x)^(n+1) ) = 0 for n>1.

%H Paul D. Hanna, <a href="/A300283/b300283.txt">Table of n, a(n) for n = 0..200</a>

%e 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 + ...

%e The table of coefficients in A( x/A(x)^(n+1) ) begins:

%e n=1: [1, 1, 2, 18, 282, 6290, 182795, 6610758, 289336014, ...];

%e n=2: [1, 1, 1, 11, 190, 4517, 137296, 5133692, 230534949, ...];

%e n=3: [1, 1, 0, 5, 113, 3030, 98861, 3875903, 180074370, ...];

%e n=4: [1, 1, -1, 0, 50, 1800, 66661, 2810026, 136890273, ...];

%e n=5: [1, 1, -2, -4, 0, 799, 39922, 1911092, 100025915, ...];

%e n=6: [1, 1, -3, -7, -38, 0, 17924, 1156423, 68624835, ...];

%e n=7: [1, 1, -4, -9, -65, -623, 0, 525528, 41924078, ...];

%e n=8: [1, 1, -5, -10, -82, -1095, -14465, 0, 19247621, ...];

%e n=9: [1, 1, -6, -10, -90, -1440, -26035, -436586, 0, ...];

%e n=10: [1, 1, -7, -9, -90, -1681, -35224, -798774, -16339863, 0, ...]; ...

%e in which the main diagonal is all zeros after the initial terms.

%o (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]}

%o for(n=0, 30, print1(a(n), ", "))

%Y Cf. A266489, A300732, A300733.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Mar 11 2018