cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A187442 A trisection of A001405 (central binomial coefficients): binomial(3*n,floor(3*n/2)), n>=0.

Original entry on oeis.org

1, 3, 20, 126, 924, 6435, 48620, 352716, 2704156, 20058300, 155117520, 1166803110, 9075135300, 68923264410, 538257874440, 4116715363800, 32247603683100, 247959266474052, 1946939425648112, 15033633249770520, 118264581564861424
Offset: 0

Views

Author

Wolfdieter Lang, Mar 10 2011

Keywords

Comments

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

Crossrefs

A187443 binomial(3*n+1,floor((3*n+1)/2)),
A187444 binomial(3*n+2,floor((3*n+2)/2))/2.

Programs

  • Mathematica
    Table[Binomial[3n,Floor[(3n)/2]],{n,0,20}] (* Harvey P. Dale, Dec 23 2012 *)

Formula

a(n) = binomial(3*n,floor(3*n/2)), n>=0.
O.g.f.: G0(x^2) + 3*x*G2(x^2) with G0(x) and G2(x) the o.g.f.s of A187363 and A187365, respectively.

A187444 A trisection of A001405 (central binomial coefficients): binomial(3n+2,floor((3n+2)/2))/2, n>=0.

Original entry on oeis.org

1, 5, 35, 231, 1716, 12155, 92378, 676039, 5200300, 38779380, 300540195, 2268783825, 17672631900, 134564468610, 1052049481860, 8061900920775, 63205303218876, 486734856412028, 3824345300380220, 29566145391215356, 232714176627630544, 1804857108504066435
Offset: 0

Views

Author

Wolfdieter Lang, Mar 10 2011

Keywords

Comments

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

Crossrefs

Cf. A187442: binomial(3*n,floor(3*n/2)), A187443: binomial(3*n+1,floor((3*n+1)/2)).

Programs

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

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.
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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