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Search: id:A039755
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| A039755 |
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Triangle of B-analogues of Stirling numbers of 2nd kind. |
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+0
11
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| 1, 1, 1, 1, 4, 1, 1, 13, 9, 1, 1, 40, 58, 16, 1, 1, 121, 330, 170, 25, 1, 1, 364, 1771, 1520, 395, 36, 1, 1, 1093, 9219, 12411, 5075, 791, 49, 1, 1, 3280, 47188, 96096, 58086, 13776, 1428, 64, 1, 1, 9841, 239220, 719860, 618870, 209622, 32340, 2388, 81, 1, 1
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Let M = an infinite lower triangular bidiagonal matrix with (1,3,5,7,...) in the main diagonal and (1,1,1,...) in the subdiagonal. n-th row = M^n * [1,0,0,0,...]. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 13 2009]
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LINKS
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R. Suter, Two analogues of a classical sequence, J. Integer Sequences, Vol. 3 (2000), #P00.1.8.
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FORMULA
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E.g.f./G.f.: exp(x + y/2 (exp(2 x) - 1))
T(n,k) = T(n-1,k-1)+(2*k+1)*T(n-1,k) with T(0,0)=T(1,0)=T(1,1)=0. sum_{k=0..n} T(n,k) = A007405(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 30 2009]
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EXAMPLE
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1; 1,1; 1,4,1; 1,13,9,1; 1,40,58,16,1; 1,121,330,170,25,1; ...
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MAPLE
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A039755 := proc(n, k) if k < 0 or k > n then 0 ; elif n <= 1 then 1; else procname(n-1, k-1)+(2*k+1)*procname(n-1, k) ; fi; end: seq(seq(A039755(n, k), k=0..n), n=0..10) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 30 2009]
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PROGRAM
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(PARI) T(n, k)=if(k<0|k>n, 0, n!*polcoeff(polcoeff(exp(x+y/2*(exp(2*x+x*O(x^n))-1)), n), k))
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CROSSREFS
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Sequence in context: A140070 A158815 A101275 this_sequence A047874 A080248 A139382
Adjacent sequences: A039752 A039753 A039754 this_sequence A039756 A039757 A039758
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KEYWORD
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nonn,tabl,new
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AUTHOR
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Ruedi Suter (suter(AT)math.ethz.ch)
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