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A255929
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Expansion of exp( Sum_{n >= 1} A210672(n)*x^n/n ).
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5
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1, 2, 15, 308, 13399, 1019106, 119698377, 20039968920, 4527610159068, 1326616296092984, 489092182592254708, 221537815033845709776, 120928125204565597029220, 78286897353506845258973144, 59305342759674536454338570652, 51970719684035315747385128783808
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OFFSET
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0,2
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COMMENTS
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It appears that this sequence is integer valued.
The o.g.f. A(x) = 1 + 2*x + 15*x^2 + 308*x^3 + ... for this sequence is such that 1 + x*d/dx( log(A(x) ) is the o.g.f. for A210672.
This sequence is the particular case m = 2 of the following general conjecture.
Let m be an integer and consider the sequence u(n) defined by the recurrence u(n) = m*Sum_{k = 0..n-1} binomial(2*n,2*k) *u(k) with the initial condition u(0) = 1. Then the expansion of exp( Sum_{n >= 1} u(n)*x^n/n ) has integer coefficients.
Note that u(n), as a polynomial in the variable m, is the n-th row generating polynomial of A241171.
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LINKS
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FORMULA
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O.g.f.: exp(2*x + 26*x^2/2 + 842*x^3/3 + 50906*x^4/4 + ...) = 1 + 2*x + 15*x^2 + 308*x^3 + 13399*x^4 + ....
a(0) = 1 and a(n) = 1/n*Sum_{k = 0..n-1} A210672(n-k)*a(k) for n >= 1.
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MAPLE
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A210672 := proc (n) option remember; if n = 0 then 1 else 2*add(binomial(2*n, 2*k)*A210672(k), k = 0 .. n-1) end if; end proc:
A255929 := proc (n) option remember; if n = 0 then 1 else add(A210672(n-k)*A255929(k), k = 0 .. n-1)/n end if; end proc:
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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