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A082580
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A sum of Lah numbers and binomial coefficients.
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0
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1, 2, 10, 68, 574, 5732, 65724, 847800, 12120966, 189890588, 3230531356, 59246895512, 1164225730540, 24387062160008, 542155626123544, 12743158072837680, 315624979700257350, 8213507146488950700
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| Formula: a(n) = Sum[ Lah[ n, k ] binomial[ 2 k, k ], { k, 0, n } ] where Lah[n, k] = binomial[ n - 1, k - 1 ] n! / k! are the Lah numbers. Recurrence: ( n + 3 ) a(n+3) - ( 3 n^2 + 17 n + 24 ) a(n+2) + 3 ( n + 3 )( n + 2 )( n + 1 ) a(n+1) - ( n + 2 )( n + 1 )^2 n a(n) = 0
E.g.f.: BesselI(0, 2*x/(1-x))*exp(2*x/(1-x)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 13 2003
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CROSSREFS
| Sequence in context: A074603 A110520 A136633 * A136658 A165968 A104098
Adjacent sequences: A082577 A082578 A082579 * A082581 A082582 A082583
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KEYWORD
| easy,nonn
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AUTHOR
| Emanuele Munarini (munarini(AT)mate.polimi.it), May 07 2003
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