A171202 G.f. A(x) satisfies A(x) = 1 + x*A(2*x)^4.

1, 1, 8, 152, 5664, 399376, 53846016, 14141384704, 7330134466560, 7551251740344320, 15510852680588984320, 63626087316632048238592, 521607805205244557347782656, 8549156556447111748331767857152, 280190094729160875643888549840814080, 18364219805837823940403573170370661842944

Offset: 0

Author

Paul D. Hanna, Dec 05 2009

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..80

Crossrefs

Cf. A135867, A171200, A171201, A171203, A171204-A171211, A343439.

Cf. A143047, A171193.

Programs

Mathematica

terms = 16; A[] = 0; Do[A[x] = 1 + x*A[2x]^4 + 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)^4); polcoeff(A, n)}

Formula

a(0) = 1; a(n) = 2^(n-1) * Sum_{i, j, k, l>=0 and i+j+k+l=n-1} a(i) * a(j) * a(k) * a(l). - Seiichi Manyama, Jul 08 2025