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A053135 Binomial coefficients C(2*n+6,6). 7
1, 28, 210, 924, 3003, 8008, 18564, 38760, 74613, 134596, 230230, 376740, 593775, 906192, 1344904, 1947792, 2760681, 3838380, 5245786, 7059052, 9366819, 12271512, 15890700, 20358520, 25827165, 32468436, 40475358, 50063860, 61474519, 74974368, 90858768 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Even indexed members of seventh column of Pascal's triangle A007318.

Number of standard tableaux of shape (2n+1,1^6). - Emeric Deutsch, May 30 2004

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 0..1000

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Milan Janjic, Two Enumerative Functions

Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

FORMULA

G.f.: (1+21*x+35*x^2+7*x^3)/(1-x)^7.

a(n) = binomial(2*n+6, 6) = A000579(2*n+6).

a(n) = A000384(n+1)*A000384(n+2)*A000384(n+3)/90. - Bruno Berselli, Nov 12 2014

E.g.f.: (90 +2430*x +6975*x^2 +5655*x^3 +1710*x^4 +204*x^5 +8*x^6)* exp(x)/90. - G. C. Greubel, Sep 03 2018

MAPLE

seq(binomial(2*n+6, 6), n=0..40); # Nathaniel Johnston, May 14 2011

MATHEMATICA

Table[Binomial[2*n+6, 6], {n, 0, 30}] (* G. C. Greubel, Sep 03 2018 *)

PROG

(PARI) vector(30, n, n--; binomial(2*n+6, 6)) \\ G. C. Greubel, Sep 03 2018

(MAGMA) [Binomial(2*n+6, 6): n in [0..30]]; // G. C. Greubel, Sep 03 2018

CROSSREFS

Cf. A000384, A000579, A002299, A053128, A053134, A190152.

Sequence in context: A159542 A244944 A155466 * A297614 A249710 A269621

Adjacent sequences:  A053132 A053133 A053134 * A053136 A053137 A053138

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified October 22 06:02 EDT 2018. Contains 316432 sequences. (Running on oeis4.)