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A167892
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a(n) = Sum[ CatalanNumber[k]^2, {k, 1, n} ].
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3
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1, 5, 30, 226, 1990, 19414, 203455, 2248355, 25887399, 307993015, 3763786811, 47032778955, 598933188955, 7751562502555, 101741582076580, 1351906409905480, 18159677984049580, 246298405721739580
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OFFSET
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1,2
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COMMENTS
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CatalanNumber[k] = (2k)!/k!/(k+1)! = Binomial[2k,k]/(k+1).
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LINKS
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Table of n, a(n) for n=1..18.
Eric Weisstein's World of Mathematics, Catalan Number
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FORMULA
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a(n) = Sum[ CatalanNumber[k]^2, {k, 1, n} ].
a(n) = Sum[ ((2k)!/k!/(k+1)!)^2, {k, 1, n} ].
a(n) = Sum[ A000108(k)^2, {k, 1, n} ].
a(n) = Sum[ A001246(k), {k, 1, n} ].
a(n) = A094639(n) - 1.
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MATHEMATICA
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Array[n \[Function] Sum[CatalanNumber[k]^2, {k, 1, n}], 20] [From J. Mulder (jasper.mulder(AT)planet.nl), Jan 25 2010]
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CROSSREFS
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Cf. A000108, A014138, A167892, A167893, A001246, A033536, A014137, A094639.
Sequence in context: A137965 A129695 A110521 * A144498 A201368 A072213
Adjacent sequences: A167889 A167890 A167891 * A167893 A167894 A167895
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KEYWORD
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more,nonn
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AUTHOR
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Alexander Adamchuk, Nov 15 2009
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EXTENSIONS
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More terms - J. Mulder (jasper.mulder(AT)planet.nl), Jan 25 2010
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STATUS
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approved
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