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Search: id:A102757
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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
1
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| 1, 4, 31, 352, 5233, 95836, 2080999, 52189096, 1482977857, 47053929268, 1648037039791, 63125834205424, 2624096058047281, 117620219281363852, 5653607876781921463, 290035426344483253816, 15814774125898034896129
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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 (jvospost2(AT)yahoo.com), Mar 17 2005
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FORMULA
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E.g.f. = 1/(1-3x)*exp(x/(1-3x))
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MAPLE
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seq(sum('binomial(k, i)^2*i!*3^i', 'i'=0..k), k=0..30);
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MATHEMATICA
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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
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Cf. A002720, A025167.
Cf. A102773.
Sequence in context: A107725 A129271 A136728 this_sequence A086677 A016036 A000314
Adjacent sequences: A102754 A102755 A102756 this_sequence A102758 A102759 A102760
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KEYWORD
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easy,nonn
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AUTHOR
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Miklos Kristof (kristmikl(AT)freemail.hu), Mar 16 2005
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 16 2005
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