A307661 E.g.f. A(x) satisfies: A(x) = exp(-x) * A(x^2)^2*A(x^3)^3*A(x^4)^4* ... *A(x^k)^k* ...

1, -1, -3, -7, -95, 699, -1739, 106973, 236097, 5525495, 157003021, -1778692191, -15439204703, -1112216292877, -2594716702395, -466679409407611, -2408062589228159, -51920010551722257, 965605721357034397, 88877767053922329545, 2657651357187708962721, 161866621274268475146539

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

E.g.f.: exp(-Sum_{k>=1} A050369(k)*x^k).

a(0) = 1; a(n) = -Sum_{k=1..n} A074206(k)*k*k!*binomial(n-1,k-1)*a(n-k).

Example

E.g.f.: A(x) = 1 - x - 3*x^2/2! - 7*x^3/3! - 95*x^4/4! + 699*x^5/5! - 1739*x^6/6! + 106973*x^7/7! + 236097*x^8/! + 5525495*x^9/9! + ...

Mathematica

terms = 21; A[_] = 1; Do[A[x_] = Exp[-x] Product[A[x^k]^k, {k, 2, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x] Range[0, terms]!

Crossrefs

Cf. A050369, A074206, A307615, A307660.

Sequence in context: A058379 A111002 A042481 * A177495 A088419 A062592

Adjacent sequences: A307658 A307659 A307660 * A307662 A307663 A307664

Keyword

sign

Author

Ilya Gutkovskiy, Apr 20 2019

Status

approved