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A059364
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Triangle T(n,k)=Sum_{i=0..n} |stirling1(n,n-i)|*binomial(i,k), k=0..n-1.
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0
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1, 2, 1, 6, 7, 2, 24, 46, 29, 6, 120, 326, 329, 146, 24, 720, 2556, 3604, 2521, 874, 120, 5040, 22212, 40564, 39271, 21244, 6084, 720, 40320, 212976, 479996, 598116, 444849, 197380, 48348, 5040, 362880, 2239344, 6023772, 9223012, 8788569
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Sum_{k=0..n-1} T(n,k)=(2*n-1)!!.
Alternating row sums = 1. - Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Aug 06 2006
Essentially triangle given by [1,1,2,2,3,3,4,4,5,5,6,6,...] DELTA [0,1,1,2,2,3,3,4,4,5,5,...] = [1;1,0;2,1,0;6,7,2,0;24,46,29,6,0;...] where DELTA is the operator defined in A084938 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 20 2006
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FORMULA
| For n>1, T(n,k) = (n-1)*T(n-1,k-1) + n*T(n-1,k) (assuming any T(i,j) outside the triangle = 0). - Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Aug 06 2006
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EXAMPLE
| [1], [2, 1], [6, 7, 2], [24, 46, 29, 6], [120, 326, 329, 146, 24], [720, 2556, 3604, 2521, 874, 120], ...
2+1=3!!, 6+7+2=5!!, 24+46+29+6=7!!, 120+326+329+146+24=9!!.
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PROG
| (PARI) T(n, k)=if(n<1, 0, n!*polcoeff(polcoeff((1-x-x*y+x*O(x^n))^(-1/(1+y)), n), k))
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CROSSREFS
| Cf. A001147, A059340.
Sequence in context: A084312 A066752 A192329 * A196554 A160348 A047708
Adjacent sequences: A059361 A059362 A059363 * A059365 A059366 A059367
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 28 2001
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