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A294037
a(n) = 4^n*hypergeom([-n/4, (1-n)/4, (2-n)/4, (3-n)/4], [1, 1, 1], -1).
2
1, 4, 16, 64, 232, 544, -1664, -37376, -362024, -2743712, -17780864, -98955776, -442825664, -1129423616, 5536033792, 118591811584, 1224814969816, 9905491019104, 68032143081856, 398051159254528, 1854461906222272, 4784426026102528
OFFSET
0,2
COMMENTS
Diagonal of rational function 1/(1 - (x^4 + y^4 + z^4 - t^4 + 4*x*y*z*t)). - Gheorghe Coserea, Aug 04 2018
FORMULA
Let H(m, n, x) = m^n*hypergeom([(k-n)/m for k=0..m-1], [1 for k=0..m-2], x) then a(n) = H(4, n, -1).
MAPLE
T := (m, n, x) -> m^n*hypergeom([seq((k-n)/m, k=0..m-1)], [seq(1, k=0..m-2)], x):
lprint(seq(simplify(T(4, n, -1)), n=0..39));
MATHEMATICA
Table[4^n * HypergeometricPFQ[{-n/4, (1-n)/4, (2-n)/4, (3-n)/4}, {1, 1, 1}, -1], {n, 0, 20}] (* Vaclav Kotesovec, Nov 02 2017 *)
CROSSREFS
H(1, n, 1) = A000007(n), H(2, n, 1) = A000984(n), H(3, n, 1) = A006077(n), H(4, n, 1) = A294036(n), H(1, n, -1) = A000079(n), H(2, n, -1) = A098335(n), H(3, n, -1) = A294035(n), H(4, n, -1) = this seq..
Sequence in context: A065738 A248089 A248088 * A228735 A289694 A232425
KEYWORD
sign
AUTHOR
Peter Luschny, Nov 02 2017
STATUS
approved