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 A259272 L.g.f.: log(G(x)/x) where G(x) is the g.f. of A259270. 3
 4, 64, 1264, 28064, 675504, 17304544, 466669536, 13155395904, 385761948592, 11725112136544, 368418702111904, 11942661856743104, 398739401015768544, 13694120483326491328, 483240865665765964224, 17505677353238744717952, 650483549418017027126704, 24776136706182576128200288 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS G.f. G(x) of A259270 satisfies: G( x - 2*G(x)*H(x) ) = x, where H'(x) = 2*G(x). LINKS Paul D. Hanna, Table of n, a(n) for n = 1..199 EXAMPLE L.g.f.: L(x) = 4*x^2/2 + 64*x^4/4 + 1264*x^6/6 + 28064*x^8/8 + 675504*x^10/10 +... where the g.f. of A259270 begins: G(x) = x*exp(L(x)) = x + 2*x^3 + 18*x^5 + 244*x^7 + 4090*x^9 + 78636*x^11 +...+ A259270(n)*x^(2*n-1) +... Now let H(x) = Integral G(x) dx, then L(x) = 2*G(x)*H(x)/x + [d/dx 4*G(x)^2*H(x)^2/x]/2! + [d^2/dx^2 8*G(x)^3*H(x)^3/x]/3! + [d^3/dx^3 16*G(x)^4*H(x)^4/x]/4! + [d^4/dx^4 32*G(x)^5*H(x)^5/x]/5! +... PROG (PARI) {a(n)=local(A=x+x*O(x^n), B=x^2); for(i=1, n, B=intformal(2*A); A = serreverse(x - 2*A*B +O(x^(2*n+2)))); 2*n*polcoeff(log(A/x), 2*n)} for(n=1, 25, print1(a(n), ", ")) CROSSREFS Cf. A259270, A259271. Sequence in context: A085807 A014729 A322519 * A085532 A146341 A264335 Adjacent sequences:  A259269 A259270 A259271 * A259273 A259274 A259275 KEYWORD nonn AUTHOR Paul D. Hanna, Jun 29 2015 STATUS approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)