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 A229548 E.g.f. satisfies: A(x) = x + A'(x) * Integral A(x) dx. 1
 1, 1, 4, 32, 412, 7664, 193080, 6308664, 259111920, 13063094736, 793227096672, 57121999975104, 4815054009921024, 469833060580971072, 52555992910144441344, 6682566041846191689984, 958596887629217123483904, 154093408614272498448416256, 27591229509407916324655477248 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 1..200 FORMULA a(n) = Sum_{k=1..n-1} binomial(n,k-1)*a(n-k)*a(k) for n>1 with a(1)=1. a(n) ~ c * (n!)^2 / (2^n * n^(1/3)), where c = 3.081214203431821156695905553610151693827575050546... - Vaclav Kotesovec, Feb 20 2014 EXAMPLE E.g.f.: A(x) = x + x^2/2! + 4*x^3/3! + 32*x^4/4! + 412*x^5/5! + 7664*x^6/6! +... such that A(x) = x + A'(x)*B(x) where A'(x) = 1 + x + 4*x^2/2! + 32*x^3/3! + 412*x^4/4! + 7664*x^5/5! +... B(x) = x^2/2! + x^3/3! + 4*x^4/4! + 32*x^5/5! + 412*x^6/6! + 7664*x^7/7! +... so that B(x) = Integral A(x) dx (here integration does not include constant term). MATHEMATICA a = ConstantArray[0, 20]; a[[1]]=1; Do[a[[n]] = Sum[Binomial[n, k-1]*a[[n-k]]*a[[k]], {k, 1, n-1}], {n, 2, 20}]; a  (* Vaclav Kotesovec, Feb 19 2014 *) PROG (PARI) {a(n)=local(A=x+x^2); for(i=1, n, A=x+A'*intformal(A+x*O(x^n))); n!*polcoeff(A, n)} for(n=1, 20, print1(a(n), ", ")) (PARI) /* Recurrence: */ {a(n)=if(n==1, 1, sum(k=1, n-1, binomial(n, k-1)*a(n-k)*a(k)))} for(n=1, 20, print1(a(n), ", ")) CROSSREFS Sequence in context: A317677 A191459 A184359 * A005172 A298694 A222685 Adjacent sequences:  A229545 A229546 A229547 * A229549 A229550 A229551 KEYWORD nonn AUTHOR Paul D. Hanna, Sep 26 2013 STATUS approved

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Last modified July 29 09:41 EDT 2021. Contains 346344 sequences. (Running on oeis4.)