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A059110
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Triangle T(n,m)= Sum_{i=0..n} L'(n,i)*binomial(i,m), m=0..n.
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5
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1, 1, 1, 3, 4, 1, 13, 21, 9, 1, 73, 136, 78, 16, 1, 501, 1045, 730, 210, 25, 1, 4051, 9276, 7515, 2720, 465, 36, 1, 37633, 93289, 85071, 36575, 8015, 903, 49, 1, 394353, 1047376, 1053724, 519456, 137270, 20048, 1596, 64, 1, 4596553, 12975561
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| L'(n,i) are unsigned Lah numbers (Cf. A008297): L'(n,i)=n!/i!*binomial(n-1,i-1) for i >= 1, L'(0,0)=1, L'(n,0)=0 for n>0. T(n,0)=A000262(n); T(n,2)=A052852(n). Row sums A052897.
Exponential Riordan array [e^(x/(1-x)),x/(1-x)]. - Paul Barry (pbarry(AT)wit.ie), Apr 28 2007
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FORMULA
| E.g.f. for T(n, m)=1/m!*(x/(1-x))^m*e^(x/(x-1)).
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EXAMPLE
| [1], [1, 1], [3, 4, 1], [13, 21, 9, 1], [73, 136, 78, 16, 1], [501, 1045, 730, 210, 25, 1], ...; E.g.f. for T(n, 2) = 1/2!*(x/(1-x))^2*e^(x/(x-1)) = 1/2*x^2 + 3/2*x^3 + 13/4*x^4 + 73/12*x^5 + 167/16*x^6 + 4051/240*x^7 + ...
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CROSSREFS
| Cf. A008297, A000262, A052852, A052897.
Sequence in context: A110506 A114189 A200659 * A100326 A028338 A039757
Adjacent sequences: A059107 A059108 A059109 * A059111 A059112 A059113
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 04 2001
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