A266489 G.f. A(x) satisfies: [x^n] A( x/A(x)^n ) = 0 for n>1.

1, 1, 2, 12, 132, 2180, 49098, 1428602, 51861128, 2290563882, 120711239660, 7471093468410, 535933804067208, 44060201848627588, 4111355981400939334, 431786985294905499210, 50663195235220478779600, 6598130071439135197135148, 948275969180128193372319072, 149616545823954331322891664338, 25794482347497414602697490580980, 4838842400288250170248755274833588

Offset

0,3

Comments

CONJECTURES:

(C1) n divides a(n) for n>=1: A268293(n) = a(n)/n.

(C2) a(n) == 0 (mod 2) for n>=2.

Links

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

Example

G.f.: A(x) = 1 + x + 2*x^2 + 12*x^3 + 132*x^4 + 2180*x^5 + 49098*x^6 + 1428602*x^7 + 51861128*x^8 + 2290563882*x^9 + 120711239660*x^10 +...
The table of coefficients in A(x/A(x)^n) begins:
n=0: [1, 1, 2, 12, 132, 2180, 49098, 1428602, 51861128, 2290563882, ...];
n=1: [1, 1, 1, 7, 85, 1511, 35891, 1086227, 40625523, 1836362991, ...];
n=2: [1, 1, 0, 3, 48, 977, 25162, 803597, 31223044, 1451879921, ...];
n=3: [1, 1, -1, 0, 20, 559, 16533, 571486, 23374922, 1126809333, ...];
n=4: [1, 1, -2, -2, 0, 239, 9662, 381746, 16837800, 852193143, ...];
n=5: [1, 1, -3, -3, -13, 0, 4242, 227238, 11400602, 620281899, ...];
n=6: [1, 1, -4, -3, -20, -174, 0, 101764, 6881536, 424405359, ...];
n=7: [1, 1, -5, -2, -22, -298, -3304, 0, 3125230, 258852007, ...];
n=8: [1, 1, -6, 0, -20, -386, -5878, -82570, 0, 118757245, ...];
n=9: [1, 1, -7, 3, -15, -451, -7899, -149719, -2604751, 0, ...];
n=10:[1, 1, -8, 7, -8, -505, -9514, -204541, -4781004, -100892514, 0, ...];
n=11:[1, 1, -9, 12, 0, -559, -10841, -249514, -6604466, -186832138, -4701375536, 0, ...]; ...
such that the main diagonal consists of 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-1)))[#A]); A[n+1]}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A268293, A300732, A300733, A300283.

Sequence in context: A215363 A200319 A213640 * A208830 A132472 A179420

Adjacent sequences: A266486 A266487 A266488 * A266490 A266491 A266492

Keyword

nonn

Author

Paul D. Hanna, Feb 07 2016

Status

approved