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
A143048
G.f. A(x) satisfies A(x) = 1 + x*A(-x)^5.
Original entry on oeis.org
1, 1, -5, -15, 165, 630, -8151, -33780, 474045, 2052495, -30206330, -134392230, 2040588775, 9248893360, -143569282680, -659546365020, 10407737293965, 48303692377425, -771991701692175, -3611789245335285, 58311219888996170, 274581478640096340
Offset: 0
A(x) = 1 + x - 5*x^2 - 15*x^3 + 165*x^4 + 630*x^5 - 8151*x^6 -++-...
A(x)^5 = 1 + 5*x - 15*x^2 - 165*x^3 + 630*x^4 + 8151*x^5 - 33780*x^6 -...
A(x)^6 = 1 + 6*x - 15*x^2 - 220*x^3 + 630*x^4 + 11286*x^5 - 33780*x^6 -...
Note that a bisection of A^6 equals a bisection of A^5.
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a(n)=local(A=x+x*O(x^n));for(i=0,n,A=1+x*subst(A,x,-x)^5);polcoeff(A,n)
A171202
G.f. A(x) satisfies A(x) = 1 + x*A(2*x)^4.
Original entry on oeis.org
1, 1, 8, 152, 5664, 399376, 53846016, 14141384704, 7330134466560, 7551251740344320, 15510852680588984320, 63626087316632048238592, 521607805205244557347782656, 8549156556447111748331767857152, 280190094729160875643888549840814080, 18364219805837823940403573170370661842944
Offset: 0
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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 *)
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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)^4); polcoeff(A, n)}
A171203
G.f. satisfies: A(x) = (1 + x*A(2x))^4.
Original entry on oeis.org
1, 4, 38, 708, 24961, 1682688, 220959136, 57266675520, 29497077110720, 30294634141775360, 62134850895148484608, 254691311135373319017472, 2087196424913845641682560512, 34202892422993270952623113994240, 1120863025258656246362522776511881216, 73460242428855296330451249854756580540416
Offset: 0
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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 *)
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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))^4); polcoeff(A, n)}
A171205
G.f. satisfies: A(x) = (1 + x*A(2x))^5.
Original entry on oeis.org
1, 5, 60, 1410, 62505, 5284401, 868838010, 281703950040, 181448450339760, 232989133846286240, 597389845561440183360, 3061032714235774931187200, 31357237236616342838622807040, 642321739861948533960660029617920, 26312068694834430629292373404100369920, 2155589935049851254662487477552439610480640
Offset: 0
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terms = 16; A[] = 0; Do[A[x] = (1 + x*A[2x])^5 + 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))^5); polcoeff(A, n)}
Showing 1-5 of 5 results.
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