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, 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

Offset: 0

Author

Paul D. Hanna, Nov 17 2011

Keywords

• nonn

Examples

			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).
		

Crossrefs

Cf. A199248, A186236, A199257, A168592, A027907.

Programs

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)}