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Search: id:A084416
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| A084416 |
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Triangle read by rows: T(n,k) = Sum_{i=k..n} i!*Stirling2(n,i), n >= 1, 1 <= k <= n. |
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+0
3
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| 1, 3, 2, 13, 12, 6, 75, 74, 60, 24, 541, 540, 510, 360, 120, 4683, 4682, 4620, 4080, 2520, 720, 47293, 47292, 47166, 45360, 36960, 20160, 5040, 545835, 545834, 545580, 539784, 498960, 372960, 181440, 40320, 7087261, 7087260, 7086750, 7068600
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Interpolates between A000670 and factorials.
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FORMULA
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E.g.f. for m-th column: (exp(x)-1)^m/(2-exp(x)). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 14 2003
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EXAMPLE
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1; 3,2; 13,12,6; 75,74,60,24; ...
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MAPLE
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T := (n, k)->add(i!*stirling2(n, i), i=k..n);
with(combinat): T := (n, k)->sum(i!*stirling2(n, i), i=k..n): seq(seq(T(n, k), k=1..n), n=1..10);
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CROSSREFS
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Mirror image of array in A084417.
Cf. A069321 (row sums).
T(n,1)=A000670(n), T(n,2)=A052875(n), T(n,n)=n!=A000142(n).
Sequence in context: A075556 A087357 A131050 this_sequence A005352 A095131 A060149
Adjacent sequences: A084413 A084414 A084415 this_sequence A084417 A084418 A084419
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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njas, Jun 24 2003
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 11 2004
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