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 A213113 E.g.f.: A(x) = exp( x/A(-x*A(x)^9)^3 ). 14
 1, 1, 7, 154, 4681, 228076, 14299129, 1138327282, 108153498625, 11945906543512, 1500579818594641, 210620216812835446, 32619162944121580369, 5512919937646519781956, 1007971183370936380058233, 197907153405452704613136466, 41467801090663272520003650049 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Compare the e.g.f. to: (1) W(x) = exp(x/W(-x*W(x)^2)^1) when W(x) = Sum_{n>=0} (1*n+1)^(n-1)*x^n/n!. (2) W(x) = exp(x/W(-x*W(x)^4)^2) when W(x) = Sum_{n>=0} (2*n+1)^(n-1)*x^n/n!. (3) W(x) = exp(x/W(-x*W(x)^6)^3) when W(x) = Sum_{n>=0} (3*n+1)^(n-1)*x^n/n!. (4) W(x) = exp(x/W(-x*W(x)^8)^4) when W(x) = Sum_{n>=0} (4*n+1)^(n-1)*x^n/n!. LINKS Table of n, a(n) for n=0..16. EXAMPLE E.g.f.: A(x) = 1 + x + 7*x^2/2! + 154*x^3/3! + 4681*x^4/4! + 228076*x^5/5! +... Related expansions: A(x)^3 = 1 + 3*x + 27*x^2/2! + 594*x^3/3! + 18873*x^4/4! + 902988*x^5/5! +... A(x)^9 = 1 + 9*x + 135*x^2/2! + 3402*x^3/3! + 121257*x^4/4! + 5887404*x^5/5! +... 1/A(-x*A(x)^9)^3 = 1 + 3*x + 45*x^2/2! + 999*x^3/3! + 39609*x^4/4! +... The logarithm of the e.g.f., log(A(x)) = x/A(-x*A(x)^9)^3, begins: log(A(x)) = x + 6*x^2/2! + 135*x^3/3! + 3996*x^4/4! + 198045*x^5/5! +... PROG (PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(x/subst(A^3, x, -x*A^9+x*O(x^n)))); n!*polcoeff(A, n)} for(n=0, 25, print1(a(n), ", ")) CROSSREFS Cf. A213108, A213109, A213110, A213111, A213112. Sequence in context: A213798 A219102 A219981 * A144683 A229711 A296232 Adjacent sequences: A213110 A213111 A213112 * A213114 A213115 A213116 KEYWORD nonn AUTHOR Paul D. Hanna, Jun 05 2012 STATUS approved

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Last modified April 19 15:11 EDT 2024. Contains 371794 sequences. (Running on oeis4.)