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A169937 Binomial(m+n-1,n)^2 - binomial(m+n,n+1)*binomial(m+n-2,n-1) with m = 14. 4
1, 91, 3185, 63700, 866320, 8836464, 71954064, 488259720, 2848181700, 14620666060, 67255063876, 281248448936, 1081724803600, 3863302870000, 12914469594000, 40680579221100, 121443493851225, 345280521733875, 938920716995625, 2451077240157000, 6162708489537600 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

13th column (and diagonal) of the triangle A001263. - Bruno Berselli, May 07 2012

REFERENCES

S. Mukai, An Introduction to Invariants and Moduli, Cambridge, 2003; Prop. 8.4, case n=14.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (25, -300, 2300, -12650, 53130, -177100, 480700, -1081575, 2042975, -3268760, 4457400, -5200300, 5200300, -4457400, 3268760, -2042975, 1081575, -480700, 177100, -53130, 12650, -2300, 300, -25, 1).

FORMULA

a(n) = (1/13)*A010965(n+12)^2*(n+13)/(n+1).  - Bruno Berselli, Nov 09 2011

a(n) = Product_{i=1..12} A002378(n+i)/A002378(i). - Bruno Berselli, Sep 01 2016

MAPLE

f:=m->[seq( binomial(m+n-1, n)^2-binomial(m+n, n+1)*binomial(m+n-2, n-1), n=0..20)]; f(14);

MATHEMATICA

Table[Binomial[13+n, n]^2-Binomial[14+n, n+1]Binomial[12+n, n-1], {n, 0, 20}] (* Harvey P. Dale, Nov 09 2011 *)

PROG

(MAGMA) [(1/13)*Binomial(n+12, 12)^2*(n+13)/(n+1): n in [0..20]];  // Bruno Berselli, Nov 09 2011

(PARI) a(n)=binomial(n+12, 12)^2*(n+13)/(n+1)/13 \\ Charles R Greathouse IV, Nov 09 2011

CROSSREFS

The expression binomial(m+n-1,n)^2-binomial(m+n,n+1)*binomial(m+n-2,n-1) for the values m = 2 through 14 produces the sequences A000012, A000217, A002415, A006542, A006857, A108679, A134288, A134289, A134290, A134291, A140925, A140935, A169937.

Cf. A002378.

Sequence in context: A008394 A221738 A133416 * A047697 A096054 A129965

Adjacent sequences:  A169934 A169935 A169936 * A169938 A169939 A169940

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Aug 28 2010

STATUS

approved

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Last modified May 25 04:50 EDT 2019. Contains 323539 sequences. (Running on oeis4.)