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A270917
Coefficient of x^n in Product_{k>=1} (1 + x^k)^(k^n).
9
1, 1, 4, 35, 457, 12421, 678101, 69540142, 13730026114, 5551573311817, 4379029522335786, 6705866900012021577, 21038900445652125741759, 131183458646068931932668114, 1603688863449847489871671547959, 40294004792352613617780682256221711
OFFSET
0,3
LINKS
FORMULA
Conjecture: limit n->infinity a(n)^(1/n^2) = exp(exp(-1)) = 1.444667861...
MAPLE
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(b(n-i*j, i-1, k)*binomial(i^k, j), j=0..n/i)))
end:
a:= n-> b(n$3):
seq(a(n), n=0..20); # Alois P. Heinz, Oct 16 2017
MATHEMATICA
Table[SeriesCoefficient[Product[(1+x^k)^(k^n), {k, 1, n}], {x, 0, n}], {n, 0, 20}]
CROSSREFS
Main diagonal of A284992.
Sequence in context: A277386 A183878 A132694 * A367925 A367923 A242795
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Mar 25 2016
STATUS
approved