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A027810 (n+1)*C(n+5,5). 11
1, 12, 63, 224, 630, 1512, 3234, 6336, 11583, 20020, 33033, 52416, 80444, 119952, 174420, 248064, 345933, 474012, 639331, 850080, 1115730, 1447160, 1856790, 2358720, 2968875, 3705156, 4587597, 5638528, 6882744 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = A245334(n+5,5)/A000142(5). - Reinhard Zumkeller, Aug 31 2014

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

Herbert John Ryser, Combinatorial Mathematics, Carus Mathematical Monographs No. 14, John Wiley and Sons, 1963, pps. 1-8.

LINKS

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

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

FORMULA

Number of 11-subsequences of [ 1, n ] with just 5 contiguous pairs.

G.f.: (1+5*x)/(1-x)^7.

MAPLE

[seq(n*(n-1)*(n-2)*(n-3)*(n-4)^2/5!, n=5..33)]; - Zerinvary Lajos, Oct 19 2006

MATHEMATICA

Table[(n+1)Binomial[n+5, 5], {n, 0, 30}] (* Harvey P. Dale, Jul 29 2014 *)

CoefficientList[Series[(1 + 5 x)/(1 - x)^7, {x, 0, 40}], x] (* Vincenzo Librandi, Jul 30 2014 *)

PROG

(MAGMA) [(n+1)*Binomial(n+5, 5): n in [0..40]] /* or */ [n*(n-1)*(n-2)*(n-3)*(n-4)^2/120: n in [5..40]]; // Vincenzo Librandi, Jul 30 2014

(Haskell)

a027810 n = (n + 1) * a007318' (n + 5) 5

-- Reinhard Zumkeller, Aug 31 2014

(PARI) a(n)=n*(n^5+16*n^4+100*n^3+310*n^2+499*n+394)/120+1 \\ Charles R Greathouse IV, Sep 28 2015

CROSSREFS

Partial sums of A051843.

Cf. A093563 ((6, 1) Pascal, column m=6).

Cf. A007813, A000142, A245334.

Sequence in context: A212249 A085463 A051922 * A012875 A275404 A162472

Adjacent sequences:  A027807 A027808 A027809 * A027811 A027812 A027813

KEYWORD

nonn,easy

AUTHOR

thi ngoc dinh (via R. K. Guy)

EXTENSIONS

Deleted two redundant formulas. - N. J. A. Sloane, Jul 30 2014

STATUS

approved

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Last modified April 21 21:03 EDT 2018. Contains 302877 sequences. (Running on oeis4.)