A384825 G.f. A(x) satisfies -1/x^29 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+10).

1, 1, 6, 54, 542, 5955, 69114, 835140, 10391843, 132262619, 1713785727, 22531557603, 299817809184, 4030217936308, 54646151953660, 746513545616000, 10264746883787021, 141955200254335604, 1973170863256461516, 27551902179444882489, 386288077655575999571, 5435910477286670671340

Offset: 0

Author

Paul D. Hanna, Jun 10 2025

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 6*x^2 + 54*x^3 + 542*x^4 + 5955*x^5 + 69114*x^6 + 835140*x^7 + 10391843*x^8 + 132262619*x^9 + 1713785727*x^10 + ...
		

Links

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

Crossrefs

Cf. A366731, A384821, A384822, A384823, A384824, A384826, A384827, A384828.

Programs

PARI

{a(n) = my(A=[1,1,0,0,0,0,0]); for(i=1, n, A = concat(A, 0);
A[#A-5] = polcoeff( sum(m=-#A, #A, x^m * Ser(A)^m * (1 - x^m +x*O(x^n))^(m+10) ), #A-36)); A[n+1]}
for(n=0, 30, print1(a(n), ", "))

Formula

G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies the following formulas.

(1) -1/x^29 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+10).

(2) -x = Sum_{n=-oo..+oo, n<>0} (-1/A(x))^n * x^((n-5)*(n-6)) / (1 - x^n)^(n-10).

a(n) ~ c * d^n / n^(3/2), where d = 15.130878695250901787504105640277512076291321821... and c = 0.088532592960846902874974330489987793829057... - Vaclav Kotesovec, Jun 11 2025