A367521 a(n) = binomial(A007310(n+1),n+1)/A007310(n+1).

1, 2, 5, 30, 99, 728, 2652, 21318, 81719, 690690, 2731365, 23841480, 96282900, 859515920, 3524015272, 31983672534, 132638171391, 1219199353190, 5101386767295, 47365474641870, 199611643133595, 1868545312633440, 7921007303554800, 74650344244967400

Offset

0,2

Comments

This sequence is related to sequence A006013.

Links

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

Formula

Limit_{n->oo, n even} a(n)/A006013(n) = 2/3.

a(n) = A006013(n) iff n is 0 or odd.

G.f.: 4F3(1/6,1/3,2/3,5/6; 1/4,3/4,3/2; (729*x^2)/16) - (2 * (4F3(-1/6,1/6,1/3,2/3; 1/4,1/2,3/4; (729*x^2)/16) - 1) / 3*x).

E.g.f.: 4F5(1/6,1/3,2/3,5/6; 1/4,1/2,3/4,1,3/2; (729*x^2)/64) + 2 * 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+1)/x; \\ Michel Marcus, Nov 22 2023

Crossrefs

Cf. A006013, A007310, A367520.

Sequence in context: A261414 A163800 A180826 * A371610 A209325 A019027

Adjacent sequences: A367518 A367519 A367520 * A367522 A367523 A367524

Keyword

nonn

Author

Miko Labalan, Nov 21 2023

Status

approved