login
A307400
G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=1} k*x^k*A(x)^k/(1 + x^k).
2
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
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 07 2019
STATUS
approved