A317913 Expansion of Product_{k>=2} (1 + k*x^k).
1, 0, 2, 3, 4, 11, 14, 29, 35, 85, 101, 187, 276, 419, 686, 1042, 1483, 2258, 3517, 4727, 7720, 10582, 15842, 21985, 32744, 45586, 65598, 93940, 131684, 183731, 260977, 357689, 500476, 699225, 946851, 1342110, 1808841, 2495154, 3375385, 4657186, 6224608, 8524443, 11468183, 15428030
Offset: 0
Keywords
Examples
a(7) = 29 because we have [7], [5, 2], [4, 3] and 7 + 5*2 + 4*3 = 29.
Links
Programs
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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]
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
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