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A100248
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Row sums of the slanted Catalan convolution table A100247.
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1
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1, 2, 10, 79, 777, 8606, 102512, 1282129, 16605538, 220781427, 2995985345, 41325515589, 577713950666, 8166924383923, 116550061698966, 1676836298476274, 24295472856858786, 354190017808427947
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OFFSET
| 0,2
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FORMULA
| a(n) = Sum_{k=0..2n} C(n+2*k-[k/2], k)*(n-[k/2])/(n+2*k-[k/2]). G.f. A(x) satisfies: A(x^2) = ((1+x)/(2-x*(1-sqrt(1-4*x)))-(1-x)/(2+x*(1-sqrt(1+4*x))))/x.
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PROG
| (PARI) {a(n)=sum(k=0, 2*n, polcoeff(((1-sqrt(1-4*z+z^2*O(z^k)))/(2*z))^(n-k\2), k, z))} (PARI) {a(n)=if(n==0, 1, sum(k=0, 2*n, binomial(n+2*k-(k\2), k)*(n-(k\2))/(n+2*k-(k\2))))}
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CROSSREFS
| Cf. A100247.
Sequence in context: A063170 A098636 A081363 * A108486 A152168 A003578
Adjacent sequences: A100245 A100246 A100247 * A100249 A100250 A100251
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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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