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A337166
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Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(1 + x - BesselI(0,2*sqrt(x))).
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1
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1, 0, -1, -1, 17, 99, -926, -20385, 25969, 7206059, 90298826, -3271747557, -149187119280, 236884125841, 233237751740057, 7110791842650002, -293292401726383791, -32980038867059802549, -498084376275585698222, 114298048468067933019627, 9072219653673352772098960
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OFFSET
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0,5
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LINKS
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FORMULA
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a(0) = 1; a(n) = -(1/n) * Sum_{k=0..n-2} binomial(n,k)^2 * (n-k) * a(k).
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MAPLE
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option remember ;
if n = 0 then
1;
else
add(binomial(n, k)^2*(n-k)*procname(k), k=0..n-2) ;
-%/n ;
end if;
simplify(%) ;
end proc:
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MATHEMATICA
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nmax = 20; CoefficientList[Series[Exp[1 + x - BesselI[0, 2 Sqrt[x]]], {x, 0, nmax}], x] Range[0, nmax]!^2
a[0] = 1; a[n_] := a[n] = -(1/n) Sum[Binomial[n, k]^2 (n - k) a[k], {k, 0, n - 2}]; Table[a[n], {n, 0, 20}]
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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