OFFSET
0,3
COMMENTS
Sum of products of terms in all partitions of n into distinct parts >= 2.
LINKS
FORMULA
G.f.: exp(Sum_{j>=1} Sum_{k>=2} (-1)^(j+1)*k^j*x^(j*k)/j).
a(n) + a(n-1) = A022629(n). - Vaclav Kotesovec, Aug 21 2018
EXAMPLE
a(7) = 29 because we have [7], [5, 2], [4, 3] and 7 + 5*2 + 4*3 = 29.
MAPLE
b:= proc(n, i) option remember; `if`(n=0 or i=1, 1,
b(n, i-1)+ i*b(n-i, min(n-i, i-1)))
end:
a:= n-> b(n$2) -`if`(n=0, 0, b(n-1$2)):
seq(a(n), n=0..50); # Alois P. Heinz, Aug 10 2018
MATHEMATICA
nmax = 43; CoefficientList[Series[Product[(1 + k x^k), {k, 2, nmax}], {x, 0, nmax}], x]
nmax = 43; CoefficientList[Series[Exp[Sum[Sum[(-1)^(j + 1) k^j x^(j k)/j, {k, 2, nmax}], {j, 1, nmax}]], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 10 2018
STATUS
approved