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 A200377 G.f.: A(x) = exp( Sum_{n>=1} [Sum_{k=0..2*n} A027907(n,k)^2 * x^k / A(x)^k]* x^n/n ). 1
 1, 1, 2, 4, 7, 11, 19, 34, 61, 106, 181, 311, 543, 955, 1668, 2885, 4980, 8650, 15114, 26391, 45845, 79385, 137718, 239866, 418338, 727926, 1263097, 2191463, 3810775, 6638258, 11556361, 20078960, 34855400, 60567092, 105405431, 183483906, 319039355, 554158992, 962743619, 1674359119, 2913758685, 5068194691 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS EXAMPLE G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 7*x^4 + 11*x^5 + 19*x^6 + 34*x^7 +... Let A = g.f. A(x), then the logarithm of the g.f. equals the series: log(A(x)) = (1 + x/A + x^2/A^2)*x + (1 + 2^2*x/A + 3^2*x^2/A^2 + 2^2*x^3/A^3 + x^4/A^4)*x^2/2 + (1 + 3^2*x/A + 6^2*x^2/A^2 + 7^2*x^3/A^3 + 6^2*x^4/A^4 + 3^2*x^5/A^5 + x^6/A^6)*x^3/3 + (1 + 4^2*x/A + 10^2*x^2/A^2 + 16^2*x^3/A^3 + 19^2*x^4/A^4 + 16^2*x^5/A^5 + 10^2*x^6/A^6 + 4^2*x^7/A^7 + x^8/A^8)*x^4/4 + (1 + 5^2*x/A + 15^2*x^2/A^2 + 30^2*x^3/A^3 + 45^2*x^4/A^4 + 51^2*x^5/A^5 + 45^2*x^6/A^6 + 30^2*x^7/A^7 + 15^2*x^8/A^8 + 5^2*x^9/A^9 + x^10/A^10)*x^5/5 +... which involves the squares of the trinomial coefficients A027907(n,k). PROG (PARI) /* G.f. A(x) using the squares of the trinomial coefficients */ {A027907(n, k)=polcoeff((1+x+x^2)^n, k)} {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, sum(k=0, 2*m, A027907(m, k)^2 *x^k/(A+x*O(x^n))^k) *x^m/m))); polcoeff(A, n)} CROSSREFS Cf. A199248, A186236, A199257, A168592, A027907. Sequence in context: A118647 A000802 A236392 * A080005 A151992 A242362 Adjacent sequences:  A200374 A200375 A200376 * A200378 A200379 A200380 KEYWORD nonn AUTHOR Paul D. Hanna, Nov 17 2011 STATUS approved

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Last modified January 27 14:39 EST 2020. Contains 331295 sequences. (Running on oeis4.)