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A098830
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3*sum(k>=0, k^n/binomial(2k, k)) = Pi*sqrt(3)*q(n)+a(n) for some rational sequence (q(n)).
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4
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0, 1, 2, 4, 10, 32, 126, 588, 3170, 19384, 132550, 1002212, 8301930, 74767056, 727348814, 7601002876, 84920459890, 1010058659048, 12742908917718, 169962226236180, 2389587638934650, 35321010036943360, 547577222471444062
(list; graph; refs; listen; history; internal format)
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OFFSET
| -1,3
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COMMENTS
| For n >= 0, this appears to be the number of permutations on n+1 elements having the "ascending-to-max" property (see He et al, Definition 2.1). - Nathaniel Johnston, Apr 10 2011
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REFERENCES
| Meng He, J. Ian Munro, and S. Srinivasa Rao, A Categorization theorem on Suffix Arrays with Applications to Space Efficient Text Indexes, SODA 2005
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = -1..180
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FORMULA
| 3*sum(k>=0, k^3/binomial(2k, k))=238/81*Pi*sqrt(3) + 32 hence a(4)=32
a(n) = Sum_{k=0..n} Sum_{j=0..n-k} (j+1)^k*Sum_{i=0..j} (-1)^(n-k+j-i)*C(j, i)*(j-i)^(n-k) (Paul D. Hanna (pauldhanna(AT)juno.com), Nov 03 2004)
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PROG
| (PARI) {a(n)=sum(k=0, n, sum(j=0, n-k, (j+1)^k*sum(i=0, j, (-1)^(n-k+j-i)*binomial(j, i)*(j-i)^(n-k))))}
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CROSSREFS
| See also A181334 and A185585.
Antidiagonal sums of array in A099594. - Ralf Stephan, Oct 28 2004
Sequence in context: A176006 A001250 A013032 * A121277 A009284 A105557
Adjacent sequences: A098827 A098828 A098829 * A098831 A098832 A098833
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 09 2004
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