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A097204
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Binomial transform of A033312.
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2
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0, 0, 1, 8, 49, 294, 1893, 13572, 109345, 985898, 9863077, 108503064, 1302057249, 16926789294, 236975148421, 3554627439308, 56874039487681, 966858672273618, 17403456103022277, 330665665961879712, 6613313319247031425
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| a(n) = Sum[n!(k!-1) / k!(n-k)! {k=0...n}]
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FORMULA
| a(n) = Sum[P(n, k) - C(n, k) {k=0...n}]
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EXAMPLE
| a(2) = 1 because P(2,0) = 1, P(2,1) = 2, P(2,2) = 2 while C(2,0) = 1, C(2,1) = 2, C(2,2) = 1 and 1 - 1 + 2 - 2 + 2 - 1 = 1.
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MAPLE
| A033312 := proc(n) factorial(n)-1; end: A097204 := proc(n) add( binomial(n, k)*A033312(k), k=1..n) ; end: seq(A097204(n), n=0..30) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 05 2007
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CROSSREFS
| Cf. A033312.
Sequence in context: A200660 A028443 A001108 * A037539 A037483 A188708
Adjacent sequences: A097201 A097202 A097203 * A097205 A097206 A097207
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KEYWORD
| nonn
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AUTHOR
| Ross La Haye (rlahaye(AT)new.rr.com), Sep 16 2004
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 05 2007
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