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 A156214 G.f.: A(x) = exp( Sum_{n>=1} 2^(n^2)*(x*A(x))^n/n ), a power series in x with integer coefficients. 2
 1, 2, 14, 256, 18734, 6932928, 11550075900, 80606017093632, 2307293302418365718, 268696321569450570148864, 126770971088210751226430473604, 241680859880056839468193961216049152 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Compare to g.f. for Catalan sequence: C(x) = exp( Sum_{n>=1} (x*C(x))^n/n ). LINKS FORMULA G.f.: A(x) = (1/x)*Series_Reversion(x/G(x)) where A(x*G(x)) = G(x) is the g.f. of A155200. [Paul D. Hanna, Jun 30 2009] EXAMPLE G.f.: A(x) = 1 + 2*x + 14*x^2 + 256*x^3 + 18734*x^4 + 6932928*x^5 +... log(A(x)) = 2*x + 24*x^2/2 + 692*x^3/3 + 72704*x^4/4 + 34465932*x^5/5 +... log(A(x)) = 2*xA(x) + 2^4*(xA(x))^2/2 + 2^9*(xA(x))^3/3 + 2^16*(xA(x))^4/4 + ... MATHEMATICA terms = 12; g[n_] := g[n] = If[n == 0, 1, (1/n)*Sum[2^(k^2)*g[n - k], {k, 1, n}]]; G[x_] = Sum[g[n]*x^n, {n, 0, terms}]; A[x_] = (1/x)*InverseSeries[Series[x/G[x], {x, 0, terms}], x]; CoefficientList[A[x] + O[x]^terms, x] (* Jean-François Alcover, Nov 14 2017 *) PROG (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=exp(sum(k=1, n, (2^k*x*A)^k/k))); polcoeff(A, n)} CROSSREFS Cf. A000108, A156213. Sequence in context: A219344 A152476 A070813 * A187654 A280517 A015197 Adjacent sequences:  A156211 A156212 A156213 * A156215 A156216 A156217 KEYWORD nonn AUTHOR Paul D. Hanna, Feb 06 2009 STATUS approved

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Last modified March 19 06:59 EDT 2018. Contains 300836 sequences. (Running on oeis4.)