A135867
G.f. satisfies A(x) = 1 + x*A(2*x)^2.
Original entry on oeis.org
1, 1, 4, 36, 640, 21888, 1451008, 188941312, 48768745472, 25069815595008, 25722272102744064, 52730972085034156032, 216091838647321476726784, 1770657164881170759078117376, 29013990909330956353981535748096
Offset: 0
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nmax = 15; A[] = 0; Do[A[x] = 1 + x*A[2*x]^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] (* Vaclav Kotesovec, Nov 04 2021 *)
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{a(n)=local(A=1+x+x*O(x^n));for(i=0,n,A=1+x*subst(A,x,2*x)^2);polcoeff(A,n)}
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a(n)=if(n==0,1,2^(n-1)*sum(k=0,n-1,a(k)*a(n-k-1))) \\ Paul D. Hanna, Feb 09 2010
A171206
G.f. A(x) satisfies A(x) = 1 + x*A(2*x)^6.
Original entry on oeis.org
1, 1, 12, 348, 19744, 2108784, 428817600, 169398274624, 131889504749568, 203937600707475456, 628561895904796999680, 3868208404121906515820544, 47571342639450113377565933568, 1169589733863427138021074362433536, 57499379103783344787572704263568097280, 5652994168279651703590653986228287051923456
Offset: 0
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terms = 16; A[] = 0; Do[A[x] = 1+x*A[2x]^6 + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Apr 02 2025 *)
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{a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*subst(A, x, 2*x)^6); polcoeff(A, n)}
A171207
G.f. satisfies: A(x) = (1 + x*A(2x))^6.
Original entry on oeis.org
1, 6, 87, 2468, 131799, 13400550, 2646848041, 1030386755856, 796631252763576, 1227659952939056640, 3777547269650299331856, 23228194648169000672639616, 285544368619000766118426358016, 7018967175754802830514246125923840, 345031382341287335424234252089128848384
Offset: 0
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terms = 15; A[] = 0; Do[A[x] = (1+x*A[2x])^6 + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Apr 02 2025 *)
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{a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=(1+x*subst(A, x, 2*x))^6); polcoeff(A, n)}
A171209
G.f. satisfies: A(x) = (1 + x*A(2x))^7.
Original entry on oeis.org
1, 7, 119, 3955, 247093, 29355725, 6770018269, 3075928905505, 2774997766597238, 4989660046676105752, 17913062958150482828608, 128508635121001835101510976, 1843071985575998120371392747776, 52855626540938653363337299348546560, 3031270298538159379928340759759663584000
Offset: 0
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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 *)
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{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)}
Showing 1-4 of 4 results.
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