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A344099
Expansion of Product_{k>=1} (1 + x^k)^binomial(k+3,4).
2
1, 1, 5, 20, 60, 190, 561, 1651, 4720, 13300, 36716, 99872, 267836, 708890, 1854255, 4796273, 12279445, 31135188, 78236006, 194921680, 481758832, 1181675902, 2877646681, 6959866116, 16723591530, 39934902812, 94795718409, 223741936855, 525206126933, 1226393510220
OFFSET
0,3
FORMULA
G.f.: exp( Sum_{k>=1} (-1)^(k+1) * x^k / (k*(1 - x^k)^5) ).
MATHEMATICA
nmax = 29; CoefficientList[Series[Product[(1 + x^k)^Binomial[k + 3, 4], {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 + 3, 4], {d, Divisors[k]}] a[n - k], {k, 1, n}]]; Table[a[n], {n, 0, 29}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 09 2021
STATUS
approved