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A100249
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Antidiagonal sums of the slanted Catalan convolution table A100247.
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1
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1, 1, 2, 3, 6, 15, 29, 63, 160, 333, 749, 1914, 4135, 9490, 24335, 53791, 125104, 321521, 721887, 1694914, 4362855, 9907851, 23429158, 60379623, 138320021, 328917615, 848432824, 1957091277, 4674847097, 12067450014, 27992976565
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n) = Sum_{k=0..[2n/3]} C(n+k-[k/2], k)*(n-k-[k/2])/(n+k-[k/2]), with a(0)=1. G.f. A(x) satisfies: A(x^2) = ((1+x)/(2*x-(1-sqrt(1-4*x^3)))-(1-x)/(2*x+(1-sqrt(1+4*x^3)))).
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PROG
| (PARI) {a(n)=if(n==0, 1, sum(k=0, (2*n)\3, binomial(n+k-(k\2), k)*(n-k-(k\2))/(n+k-(k\2))))}
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CROSSREFS
| Cf. A100247.
Sequence in context: A066653 A081945 A158027 * A138477 A052102 A053561
Adjacent sequences: A100246 A100247 A100248 * A100250 A100251 A100252
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Nov 09 2004
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