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 A177779 E.g.f.: A(x) = Sum_{n>=0} (1/n!)*Product_{k=0..n-1} L(3^k*x), where L(x) is the e.g.f. of A177780. 1
 1, 1, 7, 159, 10065, 1769889, 892392183, 1321983917631, 5822841033057825, 76645599313018616001, 3021493143896197748386407, 357064253282406274455859700319, 126544129732367263008235662373092465 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS EXAMPLE E.g.f.: A(x) = 1 + x + 7*x^2/2! + 159*x^3/3! + 10065*x^4/4! +... Then e.g.f. A(x) is given by: A(x) = 1 + L(x) + L(x)L(3x)/2! + L(x)L(3x)L(9x)/3! + L(x)L(3x)L(9x)L(27x)/4! +... where L(x) is the e.g.f. of A177780: . L(x) = x + 4*x^2/2! + 60*x^3/3! + 2496*x^4/4! + 276240*x^5/5! +... . L(x) = x*d/dx log( Sum_{n>=0} 3^(n(n-1)/2)*x^n/n! ) and satisfies: . L(x)/x = 1 + 2*L(x) + 2^2*L(x)L(3x)/2! + 2^3*L(x)L(3x)L(9x)/3! + 2^4*L(x)L(3x)L(9x)L(27x)/4! +... PROG (PARI) {a(n, q=3)=local(Lq=x+x^2, A); for(i=1, n, Lq=x*sum(m=0, n, (q-1)^m/m!*prod(k=0, m-1, subst(Lq, x, q^k*x+x*O(x^n))))); A=sum(m=0, n, 1/m!*prod(k=0, m-1, subst(Lq, x, q^k*x+x*O(x^n)))); n!*polcoeff(A, n)} CROSSREFS Cf. A177780. Sequence in context: A153714 A153713 A137995 * A177469 A121786 A316947 Adjacent sequences: A177776 A177777 A177778 * A177780 A177781 A177782 KEYWORD nonn AUTHOR Paul D. Hanna, May 20 2010 STATUS approved

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Last modified March 25 03:37 EDT 2023. Contains 361511 sequences. (Running on oeis4.)