OFFSET
0,3
COMMENTS
First differences of A006906.
Sum of products of terms in all partitions of n into parts >= 2.
LINKS
FORMULA
G.f.: exp(Sum_{j>=1} Sum_{k>=2} k^j*x^(j*k)/j).
EXAMPLE
a(6) = 31 because we have [6], [4, 2], [3, 3], [2, 2, 2] and 6 + 4*2 + 3*3 + 2*2*2 = 31.
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)))
end:
a:= n-> b(n$2) -`if`(n=0, 0, b(n-1$2)):
seq(a(n), n=0..40); # Alois P. Heinz, Aug 10 2018
MATHEMATICA
nmax = 38; CoefficientList[Series[Product[1/(1 - k x^k), {k, 2, nmax}], {x, 0, nmax}], x]
nmax = 38; CoefficientList[Series[Exp[Sum[Sum[k^j x^(j k)/j, {k, 2, nmax}], {j, 1, nmax}]], {x, 0, nmax}], x]
b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d^(k/d + 1), {d, Divisors[k]}] b[n - k], {k, 1, n}]/n]; Differences[Table[b[n], {n, -1, 38}]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 10 2018
STATUS
approved