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
A171211
G.f. satisfies: A(x) = (1 + x*A(2x))^8.
Original entry on oeis.org
1, 8, 156, 5944, 425286, 57811000, 15246040860, 7918843018760, 8165859019876353, 16781575370067304448, 68855523432488884833408, 564547878300963670909315840, 9253510119618208634494942344960
Offset: 0
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m = 13; A[] = 0; Do[A[x] = (1 + x A[2 x])^8 + O[x]^m // Normal, {m}];
CoefficientList[A[x], x] (* Jean-François Alcover, Nov 07 2019 *)
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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))^8); polcoeff(A, n)}
A171208
G.f. A(x) satisfies A(x) = 1 + x*A(2*x)^7.
Original entry on oeis.org
1, 1, 14, 476, 31640, 3953488, 939383200, 433281169216, 393718899904640, 710399428248892928, 2554705943898166145024, 18342976469146094416494592, 263185684727811758287894478848, 7549222852919288301041224694890496, 432993292623369448352459156263293419520
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)}
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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