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 A128319 G.f.: A(x) = 1+x*(1+2x*(1+3x*(...(1+n*x*(...)^3)^3...)^3)^3)^3. 4
 1, 1, 6, 66, 1034, 20790, 507600, 14546196, 478095264, 17722127700, 731393039376, 33262113690576, 1652889277811448, 89115877932595848, 5181554275409183904, 323216011162774715904, 21531610593372148573824 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS (a(n)/n!)^(1/n) tends to 4.26315... - Vaclav Kotesovec, Oct 11 2020 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..360 EXAMPLE G.f.: A(x) = 1 + x*B(x)^3; B(x) = 1 + 2*x*C(x)^3; C(x) = 1 + 3*x*D(x)^3; D(x) = 1 + 4*x*E(x)^3; E(x) = 1 + 5*x*F(x)^3; F(x) = 1 + 6*x*G(x)^3; ... where the respective sequences begin: A=[1,1,6,66,1034,20790,507600,14546196,478095264,...]; B=[1,2,18,270,5454,135936,3992544,134386344,5088220200,...]; C=[1,3,36,684,16932,504540,17367840,673851600,28994802120,...]; D=[1,4,60,1380,40460,1404000,55499040,2443032360,118003755960,...]; E=[1,5,90,2430,82350,3262770,145741680,7183818180,385393611960,...]; F=[1,6,126,3906,150234,6693120,333506880,18208871856,1075094932464,...]; G=[1,7,168,5880,253064,12523896,688855104,41282607744,2661610538160,..]; H=[1,8,216,8424,401112,21833280,1314118080,85783244400,5998813428240,..]; PROG (PARI) {a(n)=local(A=1+(n+1)*x); for(k=0, n, A=1+(n-k+1)*x*A^3 +x*O(x^n)); polcoeff(A, n)} CROSSREFS Cf. A128318. Sequence in context: A216636 A169715 A211824 * A174496 A008548 A090358 Adjacent sequences:  A128316 A128317 A128318 * A128320 A128321 A128322 KEYWORD nonn AUTHOR Paul D. Hanna, Mar 07 2007 STATUS approved

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Last modified April 12 21:47 EDT 2021. Contains 342933 sequences. (Running on oeis4.)