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 A001028 E.g.f. satisfies A'(x) = 1 + A(A(x)), A(0)=0. 10
 1, 1, 2, 7, 37, 269, 2535, 29738, 421790, 7076459, 138061343, 3089950076, 78454715107, 2238947459974, 71253947372202, 2511742808382105, 97495087989736907, 4145502184671892500, 192200099033324115855, 9676409879981926733908, 527029533717566423156698 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The e.g.f. is diverging (see the Math Overflow link). - Pietro Majer, Jan 29 2017 REFERENCES This functional equation (for f(x)=1+A(x-1)) was the subject of problem B5 of the 2010 Putnam exam. LINKS Vaclav Kotesovec, Table of n, a(n) for n = 1..320 (first 100 terms from Alois P. Heinz) P. J. Cameron, Sequence operators from groups, Linear Alg. Applic., 226-228 (1995), 109-113. Math Overflow, f' = exp(f^(-1)), again, January 2017. FORMULA E.g.f. satisfies: A(x) = Series_Reversion( Integral 1/(1 + A(x)) dx ). - Paul D. Hanna, Jun 27 2015 MAPLE A:= proc(n) option remember; local T; if n=0 then 0 else T:= A(n-1); unapply(convert(series(Int(1+T(T(x)), x), x, n+1), polynom), x) fi end: a:= n-> coeff(A(n)(x), x, n)*n!: seq(a(n), n=1..22); # Alois P. Heinz, Aug 23 2008 MATHEMATICA terms = 21; A[_] = 0; Do[A[x_] = x + Integrate[A[A[x]], x] + O[x]^(n+1) // Normal, {n, terms}]; Rest[CoefficientList[A[x], x]]*Range[terms]! (* Jean-François Alcover, Dec 07 2011, updated Jan 10 2018 *) PROG (Maxima) Co(n, k, a):= if k=1 then a(n) else sum(a(i+1)*Co(n-i-1, k-1, a), i, 0, n-k); a(n):= if n=1 then 1 else (1/n)*sum(Co(n-1, k, a)*a(k), k, 1, n-1); makelist(n!*a(n), n, 1, 7); /* Vladimir Kruchinin, Jun 30 2011 */ (PARI) {a(n) = my(A=x); for(i=1, n, A = serreverse(intformal(1/(1+A) +x*O(x^n)))); n!*polcoeff(A, n)} for(n=1, 25, print1(a(n), ", ")) \\ Paul D. Hanna, Jun 27 2015 CROSSREFS Cf. A030266, A035049. Sequence in context: A036247 A083659 A107877 * A116481 A367494 A102743 Adjacent sequences: A001025 A001026 A001027 * A001029 A001030 A001031 KEYWORD nonn,eigen,nice AUTHOR Peter J. Cameron EXTENSIONS More terms from Christian G. Bower, Oct 15 1998 Corrected by Alois P. Heinz, Aug 23 2008 Two more terms from Sean A. Irvine, Feb 22 2012 STATUS approved

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Last modified December 2 01:39 EST 2023. Contains 367505 sequences. (Running on oeis4.)