A367520 a(n) = binomial(A007310(n+1),n)/A007310(n+1).
1, 1, 3, 15, 55, 364, 1428, 10659, 43263, 345345, 1430715, 11920740, 50067108, 429757960, 1822766520, 15991836267, 68328754959, 609599676595, 2619631042665, 23682737320935, 102240109897695, 934272656316720, 4048514844039120, 37325172122483700
Offset: 0
Keywords
Programs
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PARI
f(n) = n\2*6-(-1)^n; \\ A007310 a(n) = my(x=f(n+1)); binomial(x,n)/x; \\ Michel Marcus, Nov 22 2023
Formula
Limit_{n->oo, n odd} A001764(n)/a(n) = 2/3.
a(n) = A001764(n) iff n is 1 or even.
G.f.: ((1 - 4F3(-1/6,1/6,1/3,2/3; 1/4,1/2,3/4; (729*x^2)/16)) / 3*x) + 4F3(1/6,1/3,2/3,5/6; 1/2,3/4,5/4; (729*x^2)/16).
E.g.f.: 4F5(1/6,1/3,2/3,5/6; 1/2,1/2,3/4,1,5/4; (729*x^2)/64) + x * 4F5(5/6,7/6,4/3,5/3; 5/4,3/2,3/2,7/4,2; (729*x^2)/64).
Comments