The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A107398

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A107398

a(n) = binomial(n+7, 7) * binomial(n+9, 7).
(history; published version)

#9 by Michel Marcus at Thu Sep 01 07:14:01 EDT 2022

STATUS

reviewed

approved

#8 by Joerg Arndt at Thu Sep 01 06:49:23 EDT 2022

STATUS

proposed

reviewed

#7 by Amiram Eldar at Thu Sep 01 02:13:05 EDT 2022

STATUS

editing

proposed

#6 by Amiram Eldar at Thu Sep 01 02:02:10 EDT 2022

LINKS

<a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).

FORMULA

From Amiram Eldar, Sep 01 2022: (Start)

Sum_{n>=0} 1/a(n) = 8085*Pi^2/2 - 12767311/320.

Sum_{n>=0} (-1)^n/a(n) = 245*Pi^2/4 - 580307/960. (End)

MATHEMATICA

a[n_] := Binomial[n + 7, 7] * Binomial[n + 9, 7]; Array[a, 25, 0] (* Amiram Eldar, Sep 01 2022 *)

STATUS

approved

editing

#5 by Alois P. Heinz at Fri Nov 08 20:50:19 EST 2019

STATUS

proposed

approved

#4 by Andrew Howroyd at Fri Nov 08 20:39:59 EST 2019

STATUS

editing

proposed

#3 by Andrew Howroyd at Fri Nov 08 20:20:35 EST 2019

NAME

Ca(n) = binomial(n+7, 7) *C binomial(n+9, 7).

DATA

36, 960, 11880, 950740, 95040, 566280, 2718144, 11042460, 39262080, 125147880, 364066560, 979945824, 2466996480, 5859116640, 13220570880, 28506855960, 59025960576, 117846969900, 227667211200, 426876021000, 778861512000, 1386019463400, 2410468632000, 4104188068500

LINKS

Andrew Howroyd, <a href="/A107398/b107398.txt">Table of n, a(n) for n = 0..1000</a>

EXAMPLE

If n=0 then C(n+7,7)*C(n+9,7) = C(7,7)*C(9,7) = 1*36 = 36.

If n=4 then C(4+7,7)*C(4+9,7) = C(11,7)*C(13,7) = 330*1716 = 566280.

PROG

(PARI) a(n)={binomial(n+7, 7) * binomial(n+9, 7)} \\ Andrew Howroyd, Nov 08 2019

EXTENSIONS

a(3) corrected and terms a(8) and beyond from Andrew Howroyd, Nov 08 2019

STATUS

approved

editing

#2 by N. J. A. Sloane at Wed Oct 09 09:33:28 EDT 2013

AUTHOR

_Zerinvary Lajos (zlaja(AT)freemail.hu), _, May 25 2005

Discussion

Wed Oct 09

09:33

OEIS Server: https://oeis.org/edit/global/1992

#1 by N. J. A. Sloane at Tue Jul 19 03:00:00 EDT 2005

NAME

C(n+7,7)*C(n+9,7).

DATA

36, 960, 11880, 950740, 566280, 2718144, 11042460, 39262080

OFFSET

0,1

EXAMPLE

If n=0 then C(n+7,7)*C(n+9,7)=C(7,7)*C(9,7)=1*36=36

If n=4 then C(4+7,7)*C(4+9,7)=C(11,7)*C(13,7)=330*1716=566280

CROSSREFS

Cf. A062196.

KEYWORD

easy,nonn

AUTHOR

Zerinvary Lajos (zlaja(AT)freemail.hu), May 25 2005

STATUS

approved