A195010 - OEIS

%I #5 Mar 30 2012 18:37:28

%S 1,3,42,1560,115500,14471730,2766499428,751812526080,276002969271480,

%T 131728355039531250,79330842080915572290,58863322491995284623360,

%U 52775356148028535483743372,56256397611702084409727330580,70329029468732097018514453125000

%N  a(n) = (1/n) * [x^n] 1/(1 - n^2*x)^(1/n), where [x^n] F(x) denotes the coefficient of x^n in F(x).

%e  The coefficients in (1/n)*(1 - n^2*x)^(-1/n) begin:

%e n=1: [1, (1), 1, 1, 1, 1, 1, 1, 1, 1, ...];

%e n=2: [1/2, 1,(3), 10, 35, 126, 462, 1716, 6435, 24310, ...];

%e n=3: [1/3, 1, 6, (42), 315, 2457, 19656, 160056, 1320462, ...];

%e n=4: [1/4, 1, 10, 120,(1560), 21216, 297024, 4243200, ...];

%e n=5: [1/5, 1, 15, 275, 5500,(115500), 2502500, 55412500, ...];

%e n=6: [1/6, 1, 21, 546, 15561, 466830,(14471730), 458960580, ...];

%e n=7: [1/7, 1, 28, 980, 37730, 1531838, 64337196, (2766499428), ...];

%e n=8: [1/8, 1, 36, 1632, 81600, 4308480, 235530240, 13189693440, (751812526080), ...]; ...

%e the coefficients in parenthesis form the initial terms of this sequence.

%o  (PARI) {a(n)=polcoeff(1/(1-n^2*x+x*O(x^n))^(1/n),n)/n}

%K nonn

%O 1,2

%A _Paul D. Hanna_, Sep 07 2011