A171208 G.f. A(x) satisfies A(x) = 1 + x*A(2*x)^7.

1, 1, 14, 476, 31640, 3953488, 939383200, 433281169216, 393718899904640, 710399428248892928, 2554705943898166145024, 18342976469146094416494592, 263185684727811758287894478848, 7549222852919288301041224694890496, 432993292623369448352459156263293419520

Offset: 0

Author

Paul D. Hanna, Dec 05 2009

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..79

Crossrefs

Cf. A135867, A171200-A171207, A171209, A171210-A171211, A343439.

Cf. A171196.

Programs

Mathematica

terms = 15; A[] = 0; Do[A[x] = 1+x*A[2x]^7 + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Apr 02 2025 *)

PARI

{a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*subst(A, x, 2*x)^7); polcoeff(A, n)}

Formula

a(0) = 1; a(n) = 2^(n-1) * Sum_{x_1, x_2, ..., x_7>=0 and x_1+x_2+...+x_7=n-1} Product_{k=1..7} a(x_k). - Seiichi Manyama, Jul 08 2025