A199675 - OEIS

%I #8 Mar 30 2012 18:37:32

%S 1,1,2,7,31,170,1129,8737,77198,767683,8482519,103093958,1366897597,

%T 19633740673,303706037546,5033465370031,88983532209967,

%U 1671402633292562,33241154368669921,697834148797749601,15420722865332961206,357805114894717632331,8697446048869287663271

%N E.g.f.: 1/(exp(-x) - Sum_{n>=0} (-x)^(3*n+2)/(3*n+2)!).

%F E.g.f.: A(x)=1/Q(0); Q(k)=1-x/((3*k+1)-(x^2)*(3*k+1)/((x^2)+3*(3*k+2)*(k+1)/Q(k+1)))) ; (continued fraction). - Sergei N. Gladkovskii, Nov 26 2011

%e E.g.f.: A(x) = 1 + x + 2*x^2/2! + 7*x^3/3! + 31*x^4/4! + 170*x^5/5! +...

%e where

%e A(x) = 1/(1 - x - x^3/3! + x^4/4! + x^6/6! - x^7/7! - x^9/9! + x^10/10! +...).

%o (PARI) {a(n)=n!*polcoeff(1/(exp(-x+x*O(x^n)) - sum(m=0, n\3, (-x)^(3*m+2)/(3*m+2)! )), n)}

%o (PARI) {a(n)=n!*polcoeff(1/(sum(m=0, n\3+1, (-x)^(3*m)/(3*m)! + (-x)^(3*m+1)/(3*m+1)! +x^2*O(x^n))), n)}

%Y Cf. A049774, A199670.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Nov 09 2011