The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A208961 G.f. satisfies: A(x) = 1 + x*[d/dx x/A(x)^2] 4
 1, 1, -4, 33, -376, 5255, -85392, 1566656, -31869104, 710089551, -17178977940, 448256023501, -12548355934560, 375195009917364, -11936772609109600, 402740733371490540, -14367278506882083936, 540452504929440595503, -21384560213508955184172 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..350 FORMULA G.f. A(x) satisfies: [x^n] A(x)^(2*n) = [x^n] A(x)^(2*n+1) for n>=2. a(n) ~ c * (-1)^(n+1) * n! * 2^n * n^(3/2), where c = 0.18828692660370683384... - Vaclav Kotesovec, Feb 22 2014 EXAMPLE G.f.: A(x) = 1 + x - 4*x^2 + 33*x^3 - 376*x^4 + 5255*x^5 - 85392*x^6 +... where 1/A(x)^2 = 1 - 2*x + 11*x^2 - 94*x^3 + 1051*x^4 - 14232*x^5 +... The coefficients in A(x)^n begin: n=1: [1, 1, -4, 33, -376, 5255, -85392, 1566656, ...]; n=2: [1, 2, -7, 58, -670, 9494, -156177, 2895672, ...]; n=3: [1, 3, -9, 76, -894, 12864, -214339, 4016688, ...]; n=4: [1, 4,(-10),88, -1059, 15496, -261634, 4956000, ...]; n=5: [1, 5,(-10),95, -1175, 17506, -299610, 5736885, ...]; n=6: [1, 6, -9,(98),-1251, 18996, -329626, 6379902, ...]; n=7: [1, 7, -7,(98),-1295, 20055, -352870, 6903170, ...]; n=8: [1, 8, -4, 96,(-1314),20760, -370376, 7322624, ...]; n=9: [1, 9, 0, 93,(-1314),21177, -383040, 7652250, ...]; n=10:[1,10, 5, 90, -1300,(21362),-391635, 7904300, ...]; n=11:[1,11, 11, 88, -1276,(21362),-396825, 8089488, ...]; n=12:[1,12, 18, 88, -1245, 21216,(-399178),8217168, ...]; n=13:[1,13, 26, 91, -1209, 20956,(-399178),8295495, ...]; n=14:[1,14, 35, 98, -1169, 20608, -397236,(8331570), ...]; n=15:[1,15, 45, 110,-1125, 20193, -393700,(8331570), ...]; ... where the coefficients in parenthesis demonstrate the property: [x^n] A(x)^(2*n) = [x^n] A(x)^(2*n+1) for n>=2. PROG (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*deriv(x/A^2)); polcoeff(A, n)} for(n=0, 25, print1(a(n), ", ")) CROSSREFS Cf. A185971. Sequence in context: A075132 A303919 A364439 * A113170 A187738 A198900 Adjacent sequences: A208958 A208959 A208960 * A208962 A208963 A208964 KEYWORD sign AUTHOR Paul D. Hanna, Mar 03 2012 EXTENSIONS Typo in name corrected by Vaclav Kotesovec, Feb 22 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 20 17:12 EDT 2024. Contains 371845 sequences. (Running on oeis4.)