The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A221020 Reduced denominators of A179420(n)/n!, where e.g.f. A(x) = Sum_{n>=0} A179420(n)/n! satisfies: A(A(x)) = x*A'(x) with A(0)=0, A'(0)=1. 3
 1, 1, 1, 2, 3, 6, 5, 360, 420, 56, 756, 75600, 415800, 2494800, 8424, 1223040, 504504000, 9081072000, 5145940800, 111152321280, 754247894400, 37712394720000, 430747632000, 14454741869568, 319672175961600, 4080179409546240, 14011605115200000, 1653814216454400000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS See A179420 for a description of the fascinating properties of the e.g.f. A(x) that satisfies: A(A(x)) = x*A'(x). LINKS Paul D. Hanna, Table of n, a(n) for n = 1..150 FORMULA A221019(n)/A221020(n) = A179420(n)/n!. EXAMPLE E.g.f. A(x) of A179420 begins: A(x) = x + 2*x^2/2! + 12*x^3/3! + 132*x^4/4! + 2200*x^5/5! +...+ A179420(n)/n!*x^n +... or, equivalently, A(x) = x + 1/1*x^2 + 2/1*x^3 + 11/2*x^4 + 55/3*x^5 + 419/6*x^6 + 1471/5*x^7 + 483673/360*x^8 + 2756471/420*x^9 + 1902667/56*x^10 +...+ A221019(n)/A221020(n)*x^n +... which satisfies: A(A(x)) = x*A'(x) where: A'(x) = 1 + 2*x + 12*x^2/2! + 132*x^3/3! + 2200*x^4/4! +... A(A(x)) = x + 4*x^2/2! + 36*x^3/3! + 528*x^4/4! + 11000*x^5/5! +... PROG (PARI) {A179420(n)=local(A=x+x^2+sum(m=3, n-1, A179420(m)*x^m/m!)+x*O(x^n)); if(n<3, n!*polcoeff(A, n), n!*polcoeff(subst(A, x, A), n)/(n-2))} {a(n)=denominator(A179420(n)/n!)} for(n=1, 25, print1(a(n), ", ")) CROSSREFS Cf. A221019, A179420. Sequence in context: A276087 A341837 A084678 * A333304 A248896 A102402 Adjacent sequences:  A221017 A221018 A221019 * A221021 A221022 A221023 KEYWORD nonn,frac AUTHOR Paul D. Hanna, Dec 28 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 8 11:03 EST 2021. Contains 349594 sequences. (Running on oeis4.)