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A180966 Hankel transform of A123164. 1
1, 4, 28, 384, 10496, 573440, 62652416, 13690208256, 5982889443328, 5229277301702656, 9141181343655264256, 31958984107701798174720, 223467104335874481157308416, 3125102257923487167715657908224 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..13.

FORMULA

a(n) = 2^C(n,2)*sum{k=0..floor(n/2), C(n-k,k)*(-2)^k*4^(n-2k)};

a(n) = 2^C(n,2)*[x^n](1/(1-4x+2x^2)).

a(n) = 2^(2*n+((n-1)*n)/2)*Hyper2F1([1/2-n/2, -n/2], [-n], 1/2) for n>0. - Peter Luschny, Aug 02 2014

MATHEMATICA

a[n_] := 2^Binomial[n, 2] Sum[Binomial[n-k, k] (-2)^k 4^(n-2k), {k, 0, n/2} ]; Table[a[n], {n, 0, 13}] (* Jean-Fran├žois Alcover, Jun 17 2019 *)

CROSSREFS

Sequence in context: A095288 A155105 A132685 * A203032 A086812 A197872

Adjacent sequences:  A180963 A180964 A180965 * A180967 A180968 A180969

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 29 2010

STATUS

approved

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Last modified February 23 00:28 EST 2020. Contains 332157 sequences. (Running on oeis4.)