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A102757
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Sum_{i=0..n} C(n,i)^2*i!*3^i.
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0
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1, 4, 31, 352, 5233, 95836, 2080999, 52189096, 1482977857, 47053929268, 1648037039791, 63125834205424, 2624096058047281, 117620219281363852, 5653607876781921463, 290035426344483253816, 15814774125898034896129
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Primes in this sequence include: a(2)=31, a(4)=5233. Semiprimes in this sequence include: a(1) = 2^2, a(6) = 31 * 67129, a(8) = 127 * 11676991. - Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 17 2005
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FORMULA
| E.g.f. = 1/(1-3x)*exp(x/(1-3x)).
E.g.f.: exp(3*x) * Sum_{n>=0} x^n/n!^2 = Sum_{n>=0} a(n)*x^n/n!^2. [From Paul D. Hanna, Nov 18 2011]
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MAPLE
| seq(sum('binomial(k, i)^2*i!*3^i', 'i'=0..k), k=0..30);
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MATHEMATICA
| f[n_] := Sum[k!*3^k*Binomial[n, k]^2, {k, 0, n}]; Table[ f[n], {n, 0, 16}] (* or *)
Range[0, 16]! CoefficientList[ Series[1/(1 - 3x)*Exp[x/(1 - 3x)], {x, 0, 16}], x] (from Robert G. Wilson v Mar 16 2005)
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CROSSREFS
| Cf. A002720, A025167, A102773.
Sequence in context: A145160 A129271 A136728 * A145561 A201628 A086677
Adjacent sequences: A102754 A102755 A102756 * A102758 A102759 A102760
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KEYWORD
| easy,nonn
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AUTHOR
| Miklos Kristof (kristmikl(AT)freemail.hu), Mar 16 2005
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 16 2005
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