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A344101
Expansion of Product_{k>=1} (1 + x^k)^binomial(k+5,6).
2
1, 1, 7, 35, 133, 511, 1869, 6797, 24095, 83938, 286734, 964348, 3196984, 10460310, 33813984, 108076908, 341821250, 1070484009, 3321584021, 10217036263, 31169524988, 94351439060, 283498600776, 845848778722, 2506779443603, 7381617323598, 21603241378334, 62853440151768
OFFSET
0,3
FORMULA
G.f.: exp( Sum_{k>=1} (-1)^(k+1) * x^k / (k*(1 - x^k)^7) ).
MATHEMATICA
nmax = 27; CoefficientList[Series[Product[(1 + x^k)^Binomial[k + 5, 6], {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, (1/n) Sum[Sum[(-1)^(k/d + 1) d Binomial[d + 5, 6], {d, Divisors[k]}] a[n - k], {k, 1, n}]]; Table[a[n], {n, 0, 27}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 09 2021
STATUS
approved