OFFSET
0,2
COMMENTS
This is one possible "overcomposition" analog of overpartitions (see A015128), as overpartitions are pairs of partitions and partitions into distinct parts.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
a(n) ~ c * 2^n, where c = 1.521048571756660822618351147397515199378647451699288... . - Vaclav Kotesovec, Apr 13 2017
MAPLE
c:= proc(n) c(n):= ceil(2^(n-1)) end:
b:= proc(n, i) b(n, i):= `if`(n=0, 1, `if`(i<1, 0,
expand(b(n, i-1)+`if`(i>n, 0, x*b(n-i, i-1))))) end:
d:= proc(n) d(n):= (p-> add(i!*coeff(p, x, i),
i=0..degree(p)))(b(n$2)) end:
a:= proc(n) a(n):= add(c(i)*d(n-i), i=0..n) end:
seq(a(n), n=0..35); # Alois P. Heinz, Feb 28 2014
MATHEMATICA
With[{N=66}, s=((1-q)*Sum[q^(n*(n+1)/2)*n!/QPochhammer[q, q, n], {n, 0, N}] )/(1-2*q)+O[q]^N; CoefficientList[s, q]] (* Jean-François Alcover, Jan 17 2016, adapted from PARI *)
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Joerg Arndt, Feb 27 2014
STATUS
approved