OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..3145
FORMULA
Convolution inverse of A092484.
From Vaclav Kotesovec, Sep 10 2017: (Start)
a(n) ~ (-1)^n * c * 3^(2*n/3), where
c = 0.717271758899891528435966115495396784611147877234945... if mod(n,3)=0
c = 0.387695187106751505296020614217498222070185848125472... if mod(n,3)=1
c = 0.241939482775588594057384356004734639024152664456553... if mod(n,3)=2
(End)
G.f.: exp(Sum_{k>=1} Sum_{j>=1} (-1)^k*j^(2*k)*x^(j*k)/k). - Ilya Gutkovskiy, Jun 18 2018
MAPLE
b:= proc(n, i) option remember; (m->
`if`(m<n, 0, `if`(n=m, i!^2, b(n, i-1)+
`if`(i>n, 0, i^2*b(n-i, i-1)))))(i*(i+1)/2)
end:
a:= proc(n) option remember; `if`(n=0, 1,
-add(b(n-i$2)*a(i$2), i=0..n-1))
end:
seq(a(n), n=0..40); # Alois P. Heinz, Sep 10 2017
MATHEMATICA
b[n_, i_] := b[n, i] = Function[m,
If[m < n, 0, If[n == m, i!^2, b[n, i - 1] +
If[i > n, 0, i^2*b[n - i, i - 1]]]]][i*(i + 1)/2];
a[n_] := a[n] = If[n == 0, 1, -Sum[b[n - i, n - i]*a[i], {i, 0, n - 1}]];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Mar 21 2022, after Alois P. Heinz *)
PROG
(PARI) N=66; x='x+O('x^N); Vec(1/prod(n=1, N, 1+n^2*x^n))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Sep 10 2017
STATUS
approved