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A161779
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The sequence of factorials convolved with all its regularly "aerated" variants.
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2
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1, 1, 3, 8, 30, 133, 768, 5221, 41302, 369170, 3677058, 40338310, 483134179, 6271796072, 87709287104, 1314511438945, 21017751750506, 357102350816602, 6424883282375340, 122025874117476166, 2439726373093186274, 51220112287152570828, 1126575412217509969515
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OFFSET
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0,3
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COMMENTS
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Convolve A000142 = 1,1,2,6,24,... with 1,0,1,0,2,0,6,0,24,.. and with
1,0,0,1,0,0,2,0,0,6,0,0,24,0,0,.. and with 1,0,0,0,1,0,0,0,2,0,0,0,6,... etc. ad infinitum.
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LINKS
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Table of n, a(n) for n=0..22.
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FORMULA
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Convergent of the infinite product (1,1,2,6,24,...)*(1,0,1,0,2,0,6,0,24,...)*(1,0,0,1,0,0,2,0,0,6,0,0,24,...)*...
a(n)=A096161(n). [From R. J. Mathar, Jun 26 2009]
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EXAMPLE
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Let the partial products = a, a*b, a*b*c,..., with the first few rows =
(1, 1, 2, 6, 24, 120,...) = a
(1, 1, 3, 7, 28, 128,...) = a*b
(1, 1, 3, 8, 29, 131,...) = a*b*c
(1, 1, 3, 8, 30, 132,...) = a*b*c*d
...converging to A161779
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MAPLE
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read("transforms3") ; read("transforms") ; A161779 := proc(N) local a000142, res, n, j ; a000142 := [seq(n!, n=0..N)] ; res := [seq(op(n, a000142), n=1..N)] ; for j from 1 to N do res := CONV( res, AERATE(a000142, j)) ; od: [seq(op(n, res), n=1..N)] end: A161779(30) ; # R. J. Mathar, Jun 23 2009
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CROSSREFS
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A000120
Sequence in context: A213860 A162560 A096161 * A074501 A009123 A066764
Adjacent sequences: A161776 A161777 A161778 * A161780 A161781 A161782
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson, Jun 19 2009
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EXTENSIONS
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Extended by R. J. Mathar, Jun 23 2009
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STATUS
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approved
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