A300733 G.f. A(x) satisfies: [x^n] A( x/A(x)^(3*n) ) = 0 for n>=1.

1, 1, 6, 117, 4108, 212715, 14836482, 1325939874, 147020077944, 19756725674418, 3159029077103310, 592025067793406643, 128397048202595732724, 31876577262066747598778, 8974199586989454813287292, 2841516158252445942521650875, 1004586033935983529849353475184, 394020228153801869013062325976323, 170474484645857230477080154611084378, 80943600739603137192744457809054719388

Offset

0,3

Comments

Conjecture: n divides a(n) for n>=1.

Links

Paul D. Hanna, Table of n, a(n) for n = 0..300

Example

G.f.: A(x) = 1 + x + 6*x^2 + 117*x^3 + 4108*x^4 + 212715*x^5 + 14836482*x^6 + 1325939874*x^7 + 147020077944*x^8 + 19756725674418*x^9 +...
The table of coefficients in A( x/A(x)^(3*n) ) begins:
n=0: [1, 1, 6, 117, 4108, 212715, 14836482, 1325939874, ...];
n=1: [1, 1, 3, 69, 2676, 148461, 10887243, 1010333013, ...];
n=2: [1, 1, 0, 30, 1532, 96642, 7658442, 748806253, ...];
n=3: [1, 1, -3, 0, 649, 55638, 5045967, 533295288, ...];
n=4: [1, 1, -6, -21, 0, 23910, 2954778, 356620197, ...];
n=5: [1, 1, -9, -33, -442, 0, 1298664, 212433928, ...];
n=6: [1, 1, -12, -36, -704, -17469, 0, 95171511, ...];
n=7: [1, 1, -15, -30, -813, -29793, -1010496, 0, ...];
n=8: [1, 1, -18, -15, -796, -38187, -1794006, -77230856, 0, ...]; ...
such that the main diagonal consists of all zeros after the initial terms.
The terms a(n)/n for n>=1 begin:
[1, 3, 39, 1027, 42543, 2472747, 189419982, 18377509743, 2195191741602, ...].

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)^(3*(#A-1))))[#A]); A[n+1]}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A266489, A300732.

Sequence in context: A024275 A287652 A259064 * A332627 A100070 A135869

Adjacent sequences: A300730 A300731 A300732 * A300734 A300735 A300736

Keyword

nonn

Author

Paul D. Hanna, Mar 11 2018

Status

approved