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A128321
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Column 0 of triangle A128320.
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4
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1, 1, 4, 17, 98, 622, 4512, 35373, 300974, 2722070, 26118056, 263266346, 2780054884, 30586452652, 349724463584, 4141218303165, 50678688359190, 639387728054310, 8302396672724280, 110754894628585950
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n) = Sum_{k=0..[n/2]} A000108(n-k)*A000108(k)*(k+1)!*C(n,2k) where A000108 is the Catalan numbers. a(n) = Sum_{k=0..[(n+1)/2]} C(2(n-k),n-k)/(n-k+1)*C(2k,k)/(k+1)*(k+1)!*C(n,2k).
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PROG
| (PARI) {a(n)=sum(k=0, n\2, binomial(2*n-2*k, n-k)/(n-k+1)*binomial(2*k, k)/(k+1) *(k+1)!*binomial(n, 2*k))}
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CROSSREFS
| Cf. A128320 (triangle), A128322 (column 1), A128323 (column 2), A128324 (row sums); variant: A115081.
Sequence in context: A067084 A123750 A024052 * A091635 A127676 A122940
Adjacent sequences: A128318 A128319 A128320 * A128322 A128323 A128324
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Feb 25 2007
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