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 A177778 E.g.f.: A(x) = Sum_{n>=0} 2^n/n!*Product_{k=0..n-1} L(2^k*x), where L(x) is the e.g.f. of A177777. 0
 1, 2, 12, 160, 4272, 221648, 22347648, 4416360160, 1724182065408, 1336677590208512, 2064038664552586752, 6359502604300426739200, 39136760890428640414851072, 481344480930558145524346370048 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS EXAMPLE E.g.f.: A(x) = 1 + 2*x + 12*x^2/2! + 160*x^3/3! + 4272*x^4/4! +... Then e.g.f. A(x) is given by: A(x) = 1 + 2*L(x) + 2^2*L(x)L(2x)/2! + 2^3*L(x)L(2x)L(4x)/3! + 2^4*L(x)L(2x)L(4x)L(8x)/4! +... where L(x) is the e.g.f. of A177777: . L(x) = x + 2*x^2/2! + 12*x^3/3! + 152*x^4/4! + 3640*x^5/5! +... . L(x) = x*d/dx log( Sum_{n>=0} 2^(n(n-1)/2)*x^n/n! ) and satisfies: . L(x)/x = 1 + L(x) + L(x)L(2x)/2! + L(x)L(2x)L(4x)/3! + L(x)L(2x)L(4x)L(8x)/4! +... PROG (PARI) {a(n, q=2)=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, 2^m/m!*prod(k=0, m-1, subst(Lq, x, q^k*x+x*O(x^n)))); n!*polcoeff(A, n)} CROSSREFS Cf. A177777, A177780. Sequence in context: A330552 A208577 A012646 * A180420 A012328 A302688 Adjacent sequences: A177775 A177776 A177777 * A177779 A177780 A177781 KEYWORD nonn AUTHOR Paul D. Hanna, May 20 2010 STATUS approved

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Last modified March 23 10:25 EDT 2023. Contains 361443 sequences. (Running on oeis4.)