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A027821 a(n) = 21*(n+1)*binomial(n+6,9). 1
84, 1050, 6930, 32340, 120120, 378378, 1051050, 2642640, 6126120, 13273260, 27159132, 52907400, 98760480, 177578940, 308897820, 521694096, 858049500, 1377926550, 2165313150, 3336032700, 5047562520, 7511253750, 11007400950, 15903669600, 22677454800, 31942814904 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

Number of 16-subsequences of [ 1, n ] with just 6 contiguous pairs.

LINKS

T. D. Noe, Table of n, a(n) for n = 3..1000

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

FORMULA

G.f.: 42*(2+3x)*x^3/(1-x)^11.

a(n) = C(n+1, 4)*C(n+6, 6). - Zerinvary Lajos, Jun 08 2005; corrected by R. J. Mathar, Feb 13 2016

From Amiram Eldar, Feb 03 2022: (Start)

Sum_{n>=3} 1/a(n) = 1161049/29400 - 4*Pi^2.

Sum_{n>=3} (-1)^(n+1)/a(n) = 2*Pi^2 - 1536*log(2)/35 + 104773/9800. (End)

MATHEMATICA

LinearRecurrence[{11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1}, {84, 1050, 6930, 32340, 120120, 378378, 1051050, 2642640, 6126120, 13273260, 27159132}, 30] (* Harvey P. Dale, Jul 07 2016 *)

CROSSREFS

Sequence in context: A093284 A027794 A219713 * A220049 A220210 A092719

Adjacent sequences:  A027818 A027819 A027820 * A027822 A027823 A027824

KEYWORD

nonn,easy

AUTHOR

Thi Ngoc Dinh (via R. K. Guy)

STATUS

approved

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Last modified August 16 17:52 EDT 2022. Contains 356169 sequences. (Running on oeis4.)