A246555 - OEIS

%I #15 Jul 21 2023 07:49:16

%S 1,1,1,2,5,13,36,104,309,939,2905,9118,28964,92940,300808,980864,

%T 3219205,10626023,35252867,117485454,393133485,1320357501,4449298136,

%U 15038769672,50973266380,173214422068,589998043276,2014026871496,6889055189032,23608722350440

%N a(n) = A036765(n-1) if n>0, with a(0) = 1.

%H Seiichi Manyama, <a href="/A246555/b246555.txt">Table of n, a(n) for n = 0..1000</a>

%F Given g.f. A(x), series reversion of x * A(x) = x * A210736(-x).

%F G.f.: A(x) satisfies A(x) = 1 + x * A * (1 + (A(x) - 1)^2).

%F D-finite with recurrence 2*n*(2*n+1)*a(n) +3*(7*n^2-23*n+10) *a(n-1) +12*(-8*n^2+31*n-29) *a(n-2) -16*(5*n-11)*(n-3)*a(n-3) -128*(n-3) *(n-4)*a(n-4)=0. - _R. J. Mathar_, Jul 21 2023

%e G.f. = 1 + x + x^2 + 2*x^3 + 5*x^4 + 13*x^5 + 36*x^6 + 104*x^7 + 309*x^8 + ...

%o (PARI) {a(n) = if( n<1, n==0, polcoeff( serreverse( x / (1 + x + x^2 + x^3 + x*O(x^n))), n))};

%Y Cf. A036765, A210736.

%K nonn

%O 0,4

%A _Michael Somos_, Nov 14 2014