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A262010 G.f. A(x) satisfies: A(x) = Sum_{n>=0} (4*n)!/(n!)^4 * x^n / A(x)^n. 1

%I #4 Sep 11 2015 21:43:46

%S 1,24,1944,215808,27736920,3879912960,573515224128,88128590118912,

%T 13937449300517592,2253641284021079040,370887799310890842816,

%U 61919951199385511890944,10461342569407280971842240,1785259939840128008227676160,307282893462557980175918292480,53283529423650333161886781538304,9299430498554929711121662876725720

%N G.f. A(x) satisfies: A(x) = Sum_{n>=0} (4*n)!/(n!)^4 * x^n / A(x)^n.

%C Self-convolution fourth power of A262013.

%F G.f.: x / Series_Reversion( Sum_{n>=0} (4*n)!/(n!)^4 * x^(n+1) ).

%e G.f.: A(x) = 1 + 24*x + 1944*x^2 + 215808*x^3 + 27736920*x^4 + 3879912960*x^5 +...

%e such that

%e A(x) = 1 + 24*x/A(x) + 2520*x^2/A(x)^2 + 369600*x^3/A(x)^3 + 63063000*x^4/A(x)^4 + 11732745024*x^5/A(x)^5 +...+ (4*n)!/(n!)^4 * x^n/A(x)^n +...

%o (PARI) {a(n) = local(A); A = x/serreverse( x*sum(m=0, n, (4*m)!/(m!)^4*x^m +x*O(x^n)) ) ; polcoeff(A, n)}

%o for(n=0, 20, print1(a(n), ", "))

%Y Cf. A262013, A262012.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Sep 11 2015

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Last modified March 28 17:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)