A199675 Expansion of e.g.f. 1/(exp(-x) - Sum_{n>=0} (-x)^(3*n+2)/(3*n+2)!).
1, 1, 2, 7, 31, 170, 1129, 8737, 77198, 767683, 8482519, 103093958, 1366897597, 19633740673, 303706037546, 5033465370031, 88983532209967, 1671402633292562, 33241154368669921, 697834148797749601, 15420722865332961206, 357805114894717632331, 8697446048869287663271
Offset: 0
Keywords
Examples
E.g.f.: A(x) = 1 + x + 2*x^2/2! + 7*x^3/3! + 31*x^4/4! + 170*x^5/5! +... where A(x) = 1/(1 - x - x^3/3! + x^4/4! + x^6/6! - x^7/7! - x^9/9! + x^10/10! +...).
Programs
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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)} -
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)}
Formula
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