A193098
E.g.f. A(x) satisfies: A'(x) = 1 + A(A(A(x))).
Original entry on oeis.org
1, 1, 3, 18, 171, 2283, 39942, 874944, 23243829, 731486637, 26782956144, 1124838704976, 53567894139165, 2865318598843281, 170774893724336223, 11264050942430761881, 817374450539598433587, 64917115563124199691834
Offset: 1
E.g.f.: A(x) = x + x^2/2! + 3*x^3/3! + 18*x^4/4! + 171*x^5/5! + 2283*x^6/6! +...
where the derivative of the e.g.f. begins:
A'(x) = 1 + x + 3*x^2/2! + 18*x^3/3! + 171*x^4/4! + 2283*x^5/5! +...
Related expansions.
A(A(x)) = x + 2*x^2/2! + 9*x^3/3! + 69*x^4/4! + 777*x^5/5! + 11802*x^6/6! + 229047*x^7/7! + 5472600*x^8/8! +...
A(A(A(x))) = x + 3*x^2/2! + 18*x^3/3! + 171*x^4/4! + 2283*x^5/5! +...
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{a(n)=local(A=x); for(i=1, n, A=intformal(1+subst(A, x, subst(A, x, A+O(x^(n+1)))))); n!*polcoeff(A, n)}
A193099
E.g.f. A(x) satisfies: A'(x) = 1 + A(A(A(A(x)))).
Original entry on oeis.org
1, 1, 4, 34, 466, 9044, 230827, 7388781, 287044354, 13212057907, 707417718215, 43431362340153, 3022050938855344, 236053437141340206, 20532456001485751429, 1975258248906891145913, 208928124926501980596761, 24172548454436633069025270
Offset: 1
E.g.f.: A(x) = x + x^2/2! + 4*x^3/3! + 34*x^4/4! + 466*x^5/5! + 9044*x^6/6! +...
where the derivative of the e.g.f. begins:
A'(x) = 1 + x + 4*x^2/2! + 34*x^3/3! + 466*x^4/4! + 9044*x^5/5! +...
Related expansions.
A(A(x)) = x + 2*x^2/2! + 11*x^3/3! + 111*x^4/4! + 1702*x^5/5! + 35854*x^6/6! +...
A(A(A(x))) = x + 3*x^2/2! + 21*x^3/3! + 249*x^4/4! + 4303*x^5/5! + 99650*x^6/6! +...
A(A(A(A(x)))) = x + 4*x^2/2! + 34*x^3/3! + 466*x^4/4! + 9044*x^5/5! +...
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{a(n)=local(A=x); for(i=1, n, A=intformal(1+subst(A, x, subst(A, x, subst(A, x, A+O(x^(n+1))))))); n!*polcoeff(A, n)}
Showing 1-2 of 2 results.