A187442 -id:A187442

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A187443

A trisection of A001405 (central binomial coefficients): binomial(3n+1,floor((3n+1)/2)), n>=0.

+10
2

1, 6, 35, 252, 1716, 12870, 92378, 705432, 5200300, 40116600, 300540195, 2333606220, 17672631900, 137846528820, 1052049481860, 8233430727600, 63205303218876, 495918532948104, 3824345300380220, 30067266499541040, 232714176627630544, 1832624140942590534, 14226520737620288370, 112186277816662845432, 873065282167813104916

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

For trisection of sequences see a comment and a reference under A187357.

LINKS

Table of n, a(n) for n=0..24.

FORMULA

a(n) = binomial(3*n+1,floor((3*n+1)/2)), n>=0.

O.g.f.: 3!*x*G2(x^2) + G1(x^2), with G2(x) and G1(x) the o.g.f.s of A187365 and A187364, respectively.

MATHEMATICA

Table[Binomial[3n+1, Floor[(3n+1)/2]], {n, 0, 30}] (* Harvey P. Dale, Jan 13 2021 *)

CROSSREFS

Cf. A187442: binomial(3n,floor(3n/2)), A187444: binomial(3n+2,floor((3n+2)/2))/2.

Cf. A187357, A187364, A187365.

Cf. A001405.

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Mar 10 2011

EXTENSIONS

Corrected and extended by Harvey P. Dale, Jan 13 2021

STATUS

approved

A187444

A trisection of A001405 (central binomial coefficients): binomial(3n+2,floor((3n+2)/2))/2, n>=0.

+10
2

1, 5, 35, 231, 1716, 12155, 92378, 676039, 5200300, 38779380, 300540195, 2268783825, 17672631900, 134564468610, 1052049481860, 8061900920775, 63205303218876, 486734856412028, 3824345300380220, 29566145391215356, 232714176627630544, 1804857108504066435

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

For the trisection of sequences see a comment and a reference under A187357.

LINKS

Table of n, a(n) for n=0..21.

FORMULA

a(n) = binomial(3*n+2,floor((3*n+2)/2))/2, n>=0.

O.g.f.: G1(x^2) + x*G2(x^2), with G1(x) and G2(x) the o.g.f.s of A187364 and A187366, respectively.

PROG

(PARI) vector(30, n, n--; binomial(3*n+2, (3*n+2)\2)/2) \\ Michel Marcus, Jun 11 2015