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Search: id:A115082
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| 1, 2, 5, 20, 94, 507, 3009, 19350, 132920, 966962, 7396366, 59173897, 492995320, 4262193275, 38125138575, 351960913470, 3346157796060, 32700768584100, 327957494280000, 3370522049859990, 35451669429671520, 381183654441916290
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OFFSET
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0,2
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FORMULA
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a(n) = A115081(n) + n*A115081(n-1). - Paul D. Hanna (pauldhanna(AT)juno.com), Feb 18 2007
a(n) = Sum_{k=0..[(n+1)/2]} A000108(n-k)*A000108(k)*(k+1)!*C(n+1,2k)/2^k), where A000108(n) = C(2n,n)/(n+1) is the n-th Catalan number. - Paul D. Hanna (pauldhanna(AT)juno.com), Feb 18 2007
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PROGRAM
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(PARI) {a(n)=sum(k=0, (n+1)\2, binomial(2*n-2*k, n-k)/(n-k+1)*binomial(2*k, k)/(k+1) *(k+1)!*binomial(n+1, 2*k)/2^k)} - Paul D. Hanna (pauldhanna(AT)juno.com), Feb 18 2007
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CROSSREFS
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Cf. A115080, A115081 (column 0), A115083 (column 2), A115084 (row sums); A115087.
Sequence in context: A006228 A002484 A003069 this_sequence A020105 A020005 A074415
Adjacent sequences: A115079 A115080 A115081 this_sequence A115083 A115084 A115085
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jan 13 2006
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