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A120278
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Sum[Sum[C(2k,k),{k,1,m}],{m,1,n}], where C(2k,k)=(2k)!/(k!)^2=A000984[k].
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0
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2, 10, 38, 136, 486, 1760, 6466, 24042, 90238, 341190, 1297574, 4958114, 19019254, 73196994, 282492254, 1092867904, 4236849774, 16455966944, 64020347914, 249431257704, 973100041934, 3800867789884, 14862066265434, 58170868424084
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(2(p-1)) is divisible by p^2 for p=7,13,19,31,37,43,61,67.. A002476 Primes of form 6n + 1.
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FORMULA
| a(n) = Sum[Sum[(2k)!/(k!)^2,{k,1,m}],{m,1,n}].
a(n) = 2 * Sum[ A079309[k], {k,1,n} ] = Sum[ A066796[k], {k,1,n} ]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Sep 01 2006
G.f.: x*(1/Sqrt[1-4*x]-1)/(x(x-1)^2) [From Harvey P. Dale, May 24 2011]
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MATHEMATICA
| Table[Sum[Sum[(2k)!/(k!)^2, {k, 1, m}], {m, 1, n}], {n, 1, 50}]
CoefficientList[Series[(1/Sqrt[1-4 x]-1)/((x-1)^2 x), {x, 0, 50}], x] (* From Harvey P. Dale, May 24 2011 *)
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CROSSREFS
| Cf. A000984, A066796, A002476.
Cf. A066796, A079309.
Sequence in context: A110148 A056182 A081956 * A166898 A143960 A122117
Adjacent sequences: A120275 A120276 A120277 * A120279 A120280 A120281
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KEYWORD
| nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 04 2006
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