A307396 G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=1} x^k*A(x)^k/(1 + x^k).

1, 1, 1, 4, 9, 25, 78, 235, 734, 2355, 7637, 25096, 83394, 279563, 944559, 3213254, 10996236, 37829956, 130759164, 453879479, 1581472334, 5529435704, 19393856909, 68217376618, 240586328527, 850553637256, 3013750513593, 10700805837614, 38068482070675, 135674217800041

Offset

0,4

Links

Table of n, a(n) for n=0..29.

Formula

G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=1} x^k * Sum_{d|k} (-1)^(k/d+1)*A(x)^d.

Example

G.f.: A(x) = 1 + x + x^2 + 4*x^3 + 9*x^4 + 25*x^5 + 78*x^6 + 235*x^7 + 734*x^8 + 2355*x^9 + 7637*x^10 + ...

Mathematica

terms = 30; A[_] = 0; Do[A[x_] = 1 + Sum[x^k A[x]^k /(1 + x^k), {k, 1, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
terms = 30; A[_] = 0; Do[A[x_] = 1 + Sum[x^k Sum[(-1)^(k/d + 1) A[x]^d, {d, Divisors[k]}], {k, 1, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]

Crossrefs

Cf. A048272, A192207, A192401, A307398, A307400.

Sequence in context: A176497 A304167 A317975 * A028400 A237613 A220444

Adjacent sequences: A307393 A307394 A307395 * A307397 A307398 A307399

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 07 2019

Status

approved