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G.f. satisfies: A(x) = G(x/A(x))^2 and G(x)^2 = A(x*G(x)^2) where G(x) = Sum_{n>=0} C(2n,n)*C(2n+2,n+1)/(n+2)*x^n is the g.f. of A172392.
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1, 8, 12, 0, 28, 0, 264, 0, 3720, 0, 63840, 0, 1232432, 0, 25731216, 0, 568130552, 0, 13081215840, 0, 311178567648, 0, 7597974517056, 0, 189518147463232, 0, 4811962763222784, 0, 124028853694440640, 0, 3238304402221646880, 0
G.f. satisfies: A(x) = G(x/A(x)^2) and G(x) = A(x*G(x)^2) = Sum_{n>=0} C(2n,n)*C(2n+2,n+1)/(n+2)*x^n is the g.f. of A172392.
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1, 4, -2, 8, -20, 96, -324, 1648, -6348, 33200, -137848, 732640, -3193296, 17148608, -77335400, 418289696, -1934677436, 10518803376, -49611450120, 270796872160, -1297234193744, 7102371571840, -34458382484976, 189117499963840
Triangle read by rows, a Narayana related triangle whose rows are refinements of twice the Catalan numbers (for n >= 2).
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1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 4, 4, 1, 0, 1, 7, 12, 7, 1, 0, 1, 11, 30, 30, 11, 1, 0, 1, 16, 65, 100, 65, 16, 1, 0, 1, 22, 126, 280, 280, 126, 22, 1, 0, 1, 29, 224, 686, 980, 686, 224, 29, 1, 0, 1, 37, 372, 1512, 2940, 2940, 1512, 372, 37, 1
Expansion of 3F2( (1/2, 3/2, 5/2); (3, 5))(64 x)
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1, 8, 140, 3360, 97020, 3171168, 113369256, 4338459840, 175165316040, 7385525026880, 322747443674656, 14534919841012480, 671591162296782000, 31725844951938480000, 1527939354203180010000, 74847268228930016688000, 3722092276301165621547000
Expansion of 2F1( 1/2, 3/2; 4; 16*x ).
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1, 3, 18, 140, 1260, 12474, 132132, 1472328, 17065620, 204155380, 2506399896, 31443925968, 401783498480, 5215458874500, 68633685693000, 914099013896400, 12304253831789700, 167193096184907100, 2291164651422801000, 31637804708163654000, 439903041116118980400
a(n) = 16^n*[x^n]hypergeometric([3/2, -2*n], [3], -x).
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1, 16, 480, 17920, 752640, 34062336, 1623638016, 80408739840, 4100845731840, 214072431738880, 11388653368508416, 615465127495335936, 33704042696173158400, 1866685441634205696000, 104401050057113075712000, 5889038054986331298201600, 334693662791723162114457600
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