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A101461
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Row maximum of Catalan triangle with zeros (A053121), i.e. maximum value of (m+1)*binomial(n+1,(n-m)/2)/(n+1) for given n with m same parity as n.
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0
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1, 1, 1, 2, 3, 5, 9, 14, 28, 48, 90, 165, 297, 572, 1001, 2002, 3640, 7072, 13260, 25194, 48450, 90440, 177650, 326876, 653752, 1225785, 2414425, 4601610, 8947575, 17298645, 33266625, 65132550, 124062000, 245642760, 463991880, 927983760
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| There are two maximum values when n is of the form k^2+2k-1 (i.e. 2 less than a square, A008865 offset) in which case m=k+/-1. In general m is the integer with the same parity as n closest to sqrt(n+2)-1.
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FORMULA
| a(n)=(m+1)*binomial(n+1, (n-m)/2)/(n+1) where m=floor[sqrt(n+2)-(1+(-1)^floor[n+sqrt(n+2)-1])/2]. a(n) seems to be slightly less than 2^n/n.
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CROSSREFS
| Sequence in context: A032089 A105044 A026008 * A085897 A067798 A205536
Adjacent sequences: A101458 A101459 A101460 * A101462 A101463 A101464
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KEYWORD
| nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jan 20 2005
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