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

0,3

Comments

This sequence is related to sequence A001764.

Links

Table of n, a(n) for n=0..23.

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).

Prog

(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

Crossrefs

Cf. A001764, A007310, A235534, A367521.

Sequence in context: A084152 A084175 A081951 * A346542 A033853 A284014

Adjacent sequences: A367517 A367518 A367519 * A367521 A367522 A367523

Keyword

nonn

Author

Miko Labalan, Nov 21 2023

Status

approved