A385618 G.f. A(x) satisfies A(x) = 1/( 1 - x*(A(2*x) + A(3*x)) ).

1, 2, 14, 230, 9014, 913334, 254986934, 203241812630, 471322195238102, 3214892041613961206, 64937611960188470964662, 3901256965326759127330935830, 699101347969640933511109922382422, 374397435055450676411068538643233721206, 599979003238812649083869782544110463986119734

Offset: 0

Author

Seiichi Manyama, Jul 05 2025

Keywords

• nonn

Crossrefs

Cf. A007689, A015083, A015084, A047749, A385617.

Programs

Mathematica

terms = 15; A[] = 1; Do[A[x] = 1/( 1 - x*(A[2*x] + A[3*x]) ) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Jul 05 2025 *)

PARI

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (2^j+3^j)*v[j+1]*v[i-j])); v;

Formula

a(0) = 1; a(n) = Sum_{k=0..n-1} (2^k+3^k) * a(k) * a(n-1-k).