A171197 G.f. A(x) satisfies A(x) = 1/(1 - x*A(2*x)^7).
1, 1, 15, 533, 36415, 4624621, 1108685495, 513716588981, 467874135168079, 845152554936920445, 3041003426951554000167, 21840734269889733272106629, 313415404907854466274076819391, 8990640466019774671530066108827853
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..79
Programs
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Mathematica
nmax = 15; A[] = 0; Do[A[x] = 1/(1 - x*A[2*x]^7) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] (* Vaclav Kotesovec, Nov 03 2021 *)
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PARI
{a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1/(1-x*subst(A, x, 2*x)^7) ); polcoeff(A, n)}
Formula
a(n) ~ c * 2^(n*(n-1)/2) * 7^n, where c = 0.307176924551399606223470587229647816147018... - Vaclav Kotesovec, Nov 03 2021
a(0) = 1; a(n) = 2^(n-1) * Sum_{x_1, x_2, ..., x_8>=0 and x_1+x_2+...+x_8=n-1} (1/2)^x_1 * Product_{k=1..8} a(x_k). - Seiichi Manyama, Jul 06 2025