A308369 G.f. A(x) satisfies: A(x) = x * Product_{k>=1} 1/(1 - A(x^k))^k.

1, 1, 4, 12, 41, 133, 485, 1752, 6677, 25809, 102130, 409532, 1665128, 6837348, 28333334, 118288386, 497120101, 2101181482, 8926401690, 38093403136, 163224292328, 701951448268, 3028792691947, 13108224143298, 56887750453404, 247512117880754, 1079421026637431

Offset

1,3

Links

Table of n, a(n) for n=1..27.

Formula

G.f. A(x) satisfies: A(x) = x * exp(Sum_{k>=1} Sum_{d|k} d^2 * A(x^d)^(k/d) / k).

Mathematica

terms = 27; A[_] = 0; Do[A[x_] = x Product[1/(1 - A[x^k])^k, {k, 1, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x] // Rest

Crossrefs

Cf. A050383, A091865, A308370, A308371, A308372.

Sequence in context: A180889 A002996 A076867 * A275184 A354338 A149341

Adjacent sequences: A308366 A308367 A308368 * A308370 A308371 A308372

Keyword

nonn

Author

Ilya Gutkovskiy, May 22 2019

Status

approved