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 A179496 E.g.f. satisfies: A(x) = A(x)^2*(1 + x*A(x))/(1+x) - x*A'(x). 2
 1, 1, 4, 21, 164, 1590, 18984, 266154, 4306672, 78850080, 1612769040, 36436534200, 901265930784, 24223557739056, 702975780428544, 21907246213656720, 729670520457987840, 25867686811627795200, 972505009580975483904 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A179496(n) = A179495(n+1)/(n+1). - Vaclav Kotesovec, Dec 25 2013 LINKS FORMULA Define a triangular matrix where the e.g.f. of column k equals A(x)^(k+1), then the matrix log is the matrix L with L(n+1,n)=L(n+2,n)=n+1 and zeros elsewhere. E.g.f. A(x) = G(x)/x where G(x) is the e.g.f. of A179495. a(n) ~ sqrt(1+r) * n^n * r^n / exp(n), where r = -1-LambertW(-1, -exp(-2)) = 2.146193220620582585237... is the root of the equation log(1+r)=r-1. - Vaclav Kotesovec, Jan 04 2014 EXAMPLE E.g.f. A(x) = 1 + x + 4*x^2/2! + 21*x^3/3! + 164*x^4/4! + 1590*x^5/5! +... ... Define a triangular matrix where the e.g.f. of column k = A(x)^(k+1): 1; 1, 1; 4/2!, 2, 1; 21/3!, 10/2!, 3, 1; 164/4!, 66/3!, 18/2!, 4, 1; 1590/5!, 592/4!, 141/3!, 28/2!, 5, 1; 18984/6!, 6500/5!, 1428/4!, 252/3!, 40/2!, 6, 1; 266154/7!, 85548/6!, 17430/5!, 2840/4!, 405/3!, 54/2!, 7, 1; ... then the logarithm of the above matrix equals: 0; 1, 0; 1, 2, 0; 0, 2, 3, 0; 0, 0, 3, 4, 0; 0, 0, 0, 4, 5, 0; 0, 0, 0, 0, 5, 6, 0; ... PROG (PARI) {a(n)=local(A=x+x^2+O(x^(n+1)), D=1); n!*polcoeff(1+sum(m=1, n+1, (D=A*deriv(x*D+O(x^(n+1))))/m!), n)} CROSSREFS Cf. A179495. Sequence in context: A060072 A157503 A144010 * A107872 A008858 A217484 Adjacent sequences:  A179493 A179494 A179495 * A179497 A179498 A179499 KEYWORD nonn AUTHOR Paul D. Hanna, Jul 25 2010 EXTENSIONS Name simplified by Paul D. Hanna, Jul 27 2010 Minor edits Vaclav Kotesovec, Mar 31 2014 STATUS approved

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Last modified March 21 07:23 EDT 2019. Contains 321367 sequences. (Running on oeis4.)