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Search: id:A059098
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| A059098 |
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Triangle T(n,m)=Sum_{i=0..n} stirling2(n,i)*Product_{j=1..m} (i-j+1), m=0..n. |
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+0
2
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| 1, 1, 1, 2, 3, 2, 5, 10, 12, 6, 15, 37, 62, 60, 24, 52, 151, 320, 450, 360, 120, 203, 674, 1712, 3120, 3720, 2520, 720, 877, 3263, 9604, 21336, 33600, 34440, 20160, 5040, 4140, 17007, 56674, 147756, 287784, 394800, 352800, 181440, 40320, 21147, 94828
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OFFSET
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0,4
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COMMENT
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T(n,0)=A000110; T(n,1)=A005493. Row sums give A059099.
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FORMULA
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E.g.f. for T(n, m): (e^x-1)^m*(e^(e^x-1)).
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EXAMPLE
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[1], [1, 1], [2, 3, 2], [5, 10, 12, 6], [15, 37, 62, 60, 24], [52, 151, 320, 450, 360, 120], ...; E.g.f. for T(n, 2) = (e^x-1)^2*(e^(e^x-1)) = x^2 + 2*x^3 + 31/12*x^4 + 8/3*x^5 + 107/45*x^6 + 343/180*x^7 + 28337/20160*x^8 + 349/360*x^9 + ...; E.g.f. for T(n, 3) = (e^x-1)^3*(e^(e^x-1)) = x^3 + 5/2*x^4 + 15/4*x^5 + 13/3*x^6 + 127/30*x^7 + 1759/480*x^8 + 34961/12096*x^9 + ...
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CROSSREFS
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Cf. A049020, A001861, A059099.
Sequence in context: A079535 A050159 A147294 this_sequence A082050 A162687 A010242
Adjacent sequences: A059095 A059096 A059097 this_sequence A059099 A059100 A059101
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 02 2001
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