A385622 G.f. A(x) satisfies A(x) = 1/( 1 - x*(A(x) + A(3*x))/2 ).

1, 1, 3, 20, 321, 13847, 1718124, 630600310, 691143519765, 2269026118814651, 22336295204505116859, 659523795328845920952570, 58417979762116119140729740620, 15523000838307934869469597031994180, 12374377440444177691000805646758968904928, 29593162781962095695448333383964939013238970030

Offset: 0

Author

Seiichi Manyama, Jul 05 2025

Keywords

• nonn

Crossrefs

Cf. A007051, A385617.

Cf. A385621.

Programs

Mathematica

terms = 16; A[] = 1; Do[A[x] = 1/( 1 - x*(A[x] + A[3*x])/2 )+ 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, (3^j+1)*v[j+1]*v[i-j])/2); v;

Formula

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