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 A187740 G.f.: Sum_{n>=0} (5*n+1)^n * x^n / (1 + (5*n+1)*x)^n. 8

%I #6 Jan 03 2013 01:32:14

%S 1,6,85,1650,40500,1200000,41625000,1653750000,74025000000,

%T 3685500000000,201993750000000,12084187500000000,783523125000000000,

%U 54729675000000000000,4097124281250000000000,327237848437500000000000,27775310062500000000000000,2496585341250000000000000000

%N G.f.: Sum_{n>=0} (5*n+1)^n * x^n / (1 + (5*n+1)*x)^n.

%F a(n) = (5*n+7) * 5^(n-1) * n!/2 for n>0 with a(0)=1.

%F E.g.f.: (2 - 8*x + 15*x^2) / (2*(1-5*x)^2).

%e G.f.: A(x) = 1 + 6*x + 85*x^2 + 1650*x^3 + 40500*x^4 + 1200000*x^5 +...

%e where

%e A(x) = 1 + 6*x/(1+6*x) + 11^2*x^2/(1+11*x)^2 + 16^3*x^3/(1+16*x)^3 + 21^4*x^4/(1+21*x)^4 + 26^5*x^5/(1+26*x)^5 +...

%o (PARI) {a(n)=polcoeff(sum(m=0, n, ((5*m+1)*x)^m/(1+(5*m+1)*x +x*O(x^n))^m), n)}

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

%Y Cf. A187735, A014479, A187738, A187739, A221160, A221161.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jan 03 2013

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Last modified May 19 13:25 EDT 2024. Contains 372694 sequences. (Running on oeis4.)