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 A003720 E.g.f. tan(tan(tan(x))). (Formerly M4301) 2
 1, 6, 168, 10672, 1198080, 208521728, 51874413568, 17449541107712, 7622674735988736, 4193561606973095936, 2836052065377836597248, 2312174256451088534208512, 2236165580390456719589769216, 2530976708469616321520834969600, 3314110602212685014002135203840000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 FORMULA a(n) = b(2*n+1) where b(n) = sum(m=1..n, (((-1)^(m-1)+1)*(sum(j=1..m, j! *2^(m-j-1)*(-1)^((m+1)/2+j)*S2(m,j)))*sum(k=m..n,(((-1)^(k-m)+1)*(sum(j=m..k, C(j-1,m-1)*j!*2^(k-j-1)*S2(k,j)*(-1)^((m+k)/2+j)))*((-1)^(n-k)+1)* sum(j=k,n, C(j-1,k-1)*j!*2^(n-j-1)* (-1)^((n+k)/2+j)* S2(n,j)))/k!))/m!). - Vladimir Kruchinin, Apr 23 2011 a(n) ~ 8*(2*n+1)!/((4+Pi^2) * (1+arctan(Pi/2)^2) * (arctan(arctan(Pi/2)))^(2*n+2)). - Vaclav Kotesovec, Feb 16 2015 MATHEMATICA Rest@ Union[ Range[0, 25]! CoefficientList[ Series[Tan@ Tan@ Tan@ x, {x, 0, 25}], x]] (* Robert G. Wilson v *) PROG (Maxima) a(n):=b(2*n+1); b(n):=sum((((-1)^(m-1)+1)*(sum(j!*2^(m-j-1)* (-1)^((m+1)/2+j) *stirling2(m, j), j, 1, m))*sum((((-1)^(k-m)+1)*(sum(binomial(j-1, m-1)* j!*2^(k-j-1)*stirling2(k, j)*(-1)^((m+k)/2+j), j, m, k))*((-1)^(n-k)+1)* sum(binomial(j-1, k-1)*j!*2^(n-j-1)* (-1)^((n+k)/2+j)* stirling2(n, j) , j, k, n))/k!, k, m, n))/m!, m, 1, n); [Vladimir Kruchinin, Apr 23 2011] (PARI) x='x+O('x^66); /* that many terms */ serlaplace(tan(tan(tan(x)))) /* show terms */ /* Joerg Arndt, Apr 26 2011 */ CROSSREFS Sequence in context: A106661 A322708 A181013 * A306837 A002884 A198176 Adjacent sequences:  A003717 A003718 A003719 * A003721 A003722 A003723 KEYWORD nonn AUTHOR EXTENSIONS Extended and formatted Mar 15 1997 by Olivier Gérard Corrected definition, Joerg Arndt, Apr 26 2011. a(13)-a(14) from Alois P. Heinz, May 13 2012 STATUS approved

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Last modified April 11 16:42 EDT 2021. Contains 342888 sequences. (Running on oeis4.)