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A129579
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Main diagonal of triangle A129577.
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3
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1, 1, 3, 11, 46, 213, 1075, 5854, 34141, 211974, 1394115, 9670976, 70501776, 538393812, 4294921858, 35702077464, 308575560999, 2767618399029, 25713383197122, 247072773486828, 2451716229465559, 25090920235275889
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| Equals first differences (with offset) of column 0 (A129578) of triangle A129577. Equals partial sums (with offset) of row sums (A129580) of triangle A129577.
a(n) = Sum_{k=0..n-1} a(k)*C(2*n-k-1,n-k-1)*(k+2)/(n+1) for n>0, with a(0)=1; eigensequence of triangle A033184 when the first column is omitted. [From Paul D. Hanna (pauldhanna(AT)juno.com), Aug 12 2008]
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PROG
| (PARI) a(n)=if(n==0, 1, sum(k=0, n-1, binomial(2*n-k-1, n-k-1)*(k+2)/(n+1)*a(k))) [From Paul D. Hanna (pauldhanna(AT)juno.com), Aug 12 2008]
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CROSSREFS
| Cf. A129577, A129578, A129580.
Cf. A033184. [From Paul D. Hanna (pauldhanna(AT)juno.com), Aug 12 2008]
Sequence in context: A193074 A086521 A046996 * A030814 A030976 A112567
Adjacent sequences: A129576 A129577 A129578 * A129580 A129581 A129582
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Apr 24 2007
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