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 A234296 E.g.f.: 1 + Integral (1 + Integral (1 + Integral (1 + Integral (1 + ...)^16 dx)^8 dx)^4 dx)^2 dx. 3
 1, 1, 2, 10, 112, 2544, 110944, 9088160, 1395985024, 405640228736, 225812739686144, 243825339649539840, 515865727833142919168, 2154502537039937189822464, 17852312368540223401725132800, 294428418578798287467609655705600, 9684259826489059207872454620228222976 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..80 EXAMPLE E.g.f.: A(x) = 1 + x + 2*x^2/2! + 10*x^3/3! + 112*x^4/4! + 2544*x^5/5! +... such that A(x) = 1 + Integral B(x)^2 dx, B(x) = 1 + Integral C(x)^4 dx, C(x) = 1 + Integral D(x)^8 dx, D(x) = 1 + Integral E(x)^16 dx, E(x) = 1 + Integral F(x)^32 dx, F(x) = 1 + Integral G(x)^64 dx, ... The coefficients in these series begin: A: [1, 1, 2, 10, 112, 2544, 110944, 9088160, 1395985024, ...]; B: [1, 1, 4, 44, 1048, 48472, 4171008, 663109888, 196890206720, ...]; C: [1, 1, 8, 184, 9040, 845712, 144855616, 45401856704, ...]; D: [1, 1, 16, 752, 75040, 14126752, 4830297984, 3006883867264, ...]; E: [1, 1, 32, 3040, 611392, 230931264, 157795465984, ...]; F: [1, 1, 64, 12224, 4935808, 3734695552, 5101948036608, ...]; G: [1, 1, 128, 49024, 39665920, 60075785472, 164109335366656, ...]; H: [1, 1, 256, 196352, 318046720, 963787028992, 5265107899521024, ...]; ... To illustrate a(n) = d^n/dx^n A(x) at x=0, take successive derivatives of A=A(x): A' = B^2; A'' = 2*B*C^4; A''' = 2*C^8 + 8*B*C^3*D^8; A'''' = 24*C^7*D^8 + 24*B*C^2*D^16 + 64*B*C^3*D^7*E^16; ... and then evaluate at x=0, where 1=A(0)=B(0)=C(0)=D(0)=E(0)=... PROG (PARI) {a(n)=local(A=1); for(k=0, n-1, A=1+intformal((A+x*O(x^n))^(2^(n-k)))); n!*polcoeff(A, n)} for(n=0, 20, print1(a(n), ", ")) CROSSREFS Cf. A120959, A234301. Sequence in context: A231969 A062499 A305854 * A049505 A136518 A168369 Adjacent sequences: A234293 A234294 A234295 * A234297 A234298 A234299 KEYWORD nonn AUTHOR Paul D. Hanna, Dec 24 2013 STATUS approved

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Last modified May 29 13:20 EDT 2023. Contains 363042 sequences. (Running on oeis4.)