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A059374 Triangle read by rows, T(n, k) = Sum_{i=0..n} L'(n, n-i) * binomial(i, k), for k = 0..n-1. 1
1, 3, 2, 13, 18, 6, 73, 156, 108, 24, 501, 1460, 1560, 720, 120, 4051, 15030, 21900, 15600, 5400, 720, 37633, 170142, 315630, 306600, 163800, 45360, 5040, 394353, 2107448, 4763976, 5891760, 4292400, 1834560, 423360, 40320 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
L'(n, i) are unsigned Lah numbers (Cf. A008297).
LINKS
FORMULA
E.g.f.: exp(x/(1-(1+y)*x))/(1-(1+y)*x)^2. - Vladeta Jovovic, May 10 2003
EXAMPLE
Triangle begins:
[1],
[3, 2],
[13, 18, 6],
[73, 156, 108, 24],
[501, 1460, 1560, 720, 120],
...
MATHEMATICA
t[n_, k_] := Sum[ Binomial[n-1, n-i-1]*n!/(n-i)!*Binomial[i, k], {i, 0, n}]; Table[t[n, k], {n, 1, 8}, {k, 0, n-1}] // Flatten (* Jean-François Alcover, Mar 22 2013 *)
PROG
(PARI) for(n=1, 10, for(k=0, n-1, print1(sum(j=0, n, binomial(j, k)* binomial(n-1, n-j-1)*n!/(n-j)!), ", "))) \\ G. C. Greubel, Jan 29 2018
CROSSREFS
Cf. T(n, 0) = A000262, A025168 (row sums), A000012 (alternating row sums), A059110.
Sequence in context: A005352 A095131 A060149 * A098384 A243253 A064536
KEYWORD
easy,nonn,tabl
AUTHOR
Vladeta Jovovic, Jan 28 2001
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)