A307400 G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=1} k*x^k*A(x)^k/(1 + x^k).

1, 1, 2, 9, 28, 109, 440, 1790, 7537, 32300, 140438, 618608, 2753510, 12366672, 55973926, 255059808, 1169143476, 5387268256, 24940059514, 115943355422, 541047868905, 2533458659581, 11900017205866, 56055896316345, 264748474342341, 1253414056154014, 5947373587731308

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Formula

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

Example

G.f.: A(x) = 1 + x + 2*x^2 + 9*x^3 + 28*x^4 + 109*x^5 + 440*x^6 + 1790*x^7 + 7537*x^8 + 32300*x^9 + 140438*x^10 + ...

Mathematica

terms = 27; A[_] = 0; Do[A[x_] = 1 + Sum[k x^k A[x]^k/(1 + x^k), {k, 1, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
terms = 27; A[_] = 0; Do[A[x_] = 1 + Sum[x^k Sum[(-1)^(k/d + 1) d A[x]^d, {d, Divisors[k]}], {k, 1, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]

Crossrefs

Cf. A000593, A192207, A192401, A307396, A307398.

Sequence in context: A360023 A098518 A128239 * A323682 A086511 A291632

Adjacent sequences: A307397 A307398 A307399 * A307401 A307402 A307403

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 07 2019

Status

approved