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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
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
KEYWORD
sign
AUTHOR
Paul D. Hanna, Mar 03 2012
EXTENSIONS
Typo in name corrected by Vaclav Kotesovec, Feb 22 2014
STATUS
approved

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