A195010 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).

1, 3, 42, 1560, 115500, 14471730, 2766499428, 751812526080, 276002969271480, 131728355039531250, 79330842080915572290, 58863322491995284623360, 52775356148028535483743372, 56256397611702084409727330580, 70329029468732097018514453125000

Offset

1,2

Links

Table of n, a(n) for n=1..15.

Example

 The coefficients in (1/n)*(1 - n^2*x)^(-1/n) begin:
n=1: [1, (1), 1, 1, 1, 1, 1, 1, 1, 1, ...];
n=2: [1/2, 1,(3), 10, 35, 126, 462, 1716, 6435, 24310, ...];
n=3: [1/3, 1, 6, (42), 315, 2457, 19656, 160056, 1320462, ...];
n=4: [1/4, 1, 10, 120,(1560), 21216, 297024, 4243200, ...];
n=5: [1/5, 1, 15, 275, 5500,(115500), 2502500, 55412500, ...];
n=6: [1/6, 1, 21, 546, 15561, 466830,(14471730), 458960580, ...];
n=7: [1/7, 1, 28, 980, 37730, 1531838, 64337196, (2766499428), ...];
n=8: [1/8, 1, 36, 1632, 81600, 4308480, 235530240, 13189693440, (751812526080), ...]; ...
the coefficients in parenthesis form the initial terms of this sequence.

Prog

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

Crossrefs

Sequence in context: A078601 A268621 A218308 * A333323 A331705 A156108

Adjacent sequences: A195007 A195008 A195009 * A195011 A195012 A195013

Keyword

nonn

Author

Paul D. Hanna, Sep 07 2011

Status

approved