A246555 a(n) = A036765(n-1) if n>0, with a(0) = 1.

1, 1, 1, 2, 5, 13, 36, 104, 309, 939, 2905, 9118, 28964, 92940, 300808, 980864, 3219205, 10626023, 35252867, 117485454, 393133485, 1320357501, 4449298136, 15038769672, 50973266380, 173214422068, 589998043276, 2014026871496, 6889055189032, 23608722350440

Offset: 0

Author

Michael Somos, Nov 14 2014

Keywords

• nonn

Examples

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

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A036765, A210736.

Programs

PARI

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

Formula

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

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

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