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A102773
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a(n) = Sum_{i=0..n} binomial(n,i)^2*i!*4^i.
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7
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1, 5, 49, 709, 13505, 318181, 8916145, 289283429, 10656031489, 439039941445, 19995858681521, 997184081617285, 54026137182982849, 3159127731435043109, 198258247783634075185, 13289190424904891606821, 947419111092028780186625
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OFFSET
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0,2
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LINKS
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FORMULA
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E.g.f.: (1/(1-4x))*exp(x/(1-4x)).
a(n) ~ n^(n+1/4) * exp(sqrt(n)-n-1/8) * 4^n * (1 + 37/(96*sqrt(n))). - Vaclav Kotesovec, Oct 09 2013
Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(4*x) * BesselI(0,2*sqrt(x)). - Ilya Gutkovskiy, Jul 17 2020
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MAPLE
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seq(sum('binomial(k, i)^2*i!*4^i', 'i'=0..k), k=0..30);
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MATHEMATICA
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f[n_] := Sum[k!*4^k*Binomial[n, k]^2, {k, 0, n}]; Table[ f[n], {n, 0, 16}] (* or *)
Range[0, 16]! CoefficientList[ Series[1/(1 - 4x)*Exp[x/(1 - 4x)], {x, 0, 16}], x] (* Robert G. Wilson v, Mar 16 2005 *)
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PROG
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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