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A055462
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Superduperfactorials: product of first n superfactorials.
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9
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1, 1, 2, 24, 6912, 238878720, 5944066965504000, 745453331864786829312000000, 3769447945987085350501386572267520000000000, 6916686207999802072984424331678589933649915805696000000000000000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Next term is 46055492324773905212722208920097589966225904305970614833621406622679040000000000000000000000 (92 characters) [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 13 2009]
Contribution from Peter Luschny (peter(AT)luschny.de), Jul 14 2009: (Start)
Starting with offset 1, a(n) is a 'Matryoshka doll' sequence with alpha=1, the mutiplicative counterpart to the additive A000332.
seq(mul(mul(mul(i,i=alpha..k),k=alpha..n),n=alpha..m),m=alpha..10). (End)
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FORMULA
| a(n) = a(n-1)*A000178(n) = Product[(i!)^(n-i+1)] over 1 <= i <= n = Product[i^((n-i+1)(n-i+2)/2)] over 1 <= i <= n
log a(n) = (1/6) n^3 log n - (11/36) n^3 + O(n^2 log n). [Charles R Greathouse IV, Jan 13 2012]
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EXAMPLE
| a(4) = 1!2!3!4!*1!2!3!*1!2!*1! = 288*12*2*1 = 6912
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MATHEMATICA
| s1=1; s2=1; lst={}; Do[f=n!; s1*=f; s2*=s1; AppendTo[lst, s2], {n, 0, 3*3!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 13 2009]
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PROG
| (PARI) a(n)=my(t=1); prod(k=2, n, t*=k!) \\ Charles R Greathouse IV, Jul 28 2011
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CROSSREFS
| Cf. A000142, A000178, A002109.
Sequence in context: A159907 A088912 A203465 * A088600 A066120 A152687
Adjacent sequences: A055459 A055460 A055461 * A055463 A055464 A055465
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KEYWORD
| nonn,easy
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jun 26 2000
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EXTENSIONS
| a(9) from N. J. A. Sloane (njas(AT)research.att.com), Dec 15 2008
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