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A174324 a(n) = 3F0(-n,-n+1,-n+2;;-1/2) = n!*(n-1)!*2^(1-n)* 1F2(-n+2;2,3;-2), where nFm(;;) are generalized hypergeometric series. 0
1, 4, 31, 391, 7261, 185956, 6271189, 269066701, 14300511481, 921666527596, 70789188893611, 6386088654729499, 668423261212035421, 80325071500899911596, 10981857825124725031081, 1694577083441728891610041 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

Table of n, a(n) for n=2..17.

FORMULA

The sequence a(n) can be obtained from the following three generating functions of hypergeometric type:

g1(t) = sum(a(n)*t^n/(n!*(n-1)!),n=2..infinity) = (t^2/(1-t/2))* 1F2(1;2,3;t/(1-t/2))/2.

g2(t) = sum(a(n)*t^n/(n!*(n-1)!*(n-2)!), n=2..infinity) = exp(t/2)*t^2* 0F2(;2,3;t)/2.

g3(t) = sum(a(n)*t^n/(n!*(n-1)!*(n-2)), n=3..infinity) = t^2*(t/(6*(1-t/2))* 2F3(1,1;2,3,4;t/(1-t/2))-log(1-t/2))/2.

Note the appearance of the factor (n-2) and not (n-2)! in the denominator of g3.

CROSSREFS

Sequence in context: A215529 A005046 A323568 * A211194 A237581 A319074

Adjacent sequences:  A174321 A174322 A174323 * A174325 A174326 A174327

KEYWORD

nonn

AUTHOR

Karol A. Penson and Katarzyna Gorska, Mar 15 2010

STATUS

approved

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Last modified May 22 14:32 EDT 2019. Contains 323480 sequences. (Running on oeis4.)