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A002299 Binomial coefficients C(2*n+5,5). 6
1, 21, 126, 462, 1287, 3003, 6188, 11628, 20349, 33649, 53130, 80730, 118755, 169911, 237336, 324632, 435897, 575757, 749398, 962598, 1221759, 1533939, 1906884, 2349060, 2869685, 3478761, 4187106, 5006386, 5949147, 7028847, 8259888, 9657648, 11238513 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of standard tableaux of shape (2n+1,1^5). - Emeric Deutsch, May 30 2004

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000 (terms 0..200 from Vincenzo Librandi)

Milan Janjic, Two Enumerative Functions

J. M. Landsberg and L. Manivel, The sextonions and E7 1/2, Adv. Math. 201 (2006), 143-179. [Th. 7.2(i), case a=1]

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

a(n) = A000389(2*n+5).

G.f.: (1+15*x+15*x^2+x^3)/(1-x)^6 = (1+x)*(x^2+14*x+1)/(1-x)^6.

E.g.f.: (30 + 600*x + 1275*x^2 + 730*x^3 + 140*x^4 + 8*x^5)*exp(x)/30. - G. C. Greubel, Nov 23 2017

MATHEMATICA

Table[Binomial[2*n + 5, 5], {n, 0, 50}] (* G. C. Greubel, Nov 23 2017 *)

PROG

(MAGMA) [Binomial(2*n+5, 5): n in [0..30]]; // Vincenzo Librandi, Oct 07 2011

(PARI) a(n)=n*(8*n^4+60*n^3+170*n^2+225*n+137)/30+1 \\ Charles R Greathouse IV, Apr 18 2012

CROSSREFS

Cf. A000389, A053127.

Sequence in context: A117388 A053052 A243882 * A213565 A041852 A220712

Adjacent sequences:  A002296 A002297 A002298 * A002300 A002301 A002302

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Eric Lane (ericlane(AT)utcvm.utc.edu)

STATUS

approved

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Last modified February 21 07:18 EST 2018. Contains 299390 sequences. (Running on oeis4.)