A027813 - OEIS

A027813

a(n) = 14*(n+1)*binomial(n+5,8).

56, 630, 3780, 16170, 55440, 162162, 420420, 990990, 2162160, 4424420, 8576568, 15872220, 28217280, 48430620, 80582040, 130423524, 205931880, 317983050, 481180700, 714864150, 1044323280, 1502250750, 2130464700, 2981938050, 4123173600, 5636967336, 7625605680

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OFFSET

3,1

COMMENTS

Number of 14-subsequences of [ 1, n ] with just 5 contiguous pairs.

LINKS

Table of n, a(n) for n=3..29.

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

FORMULA

G.f.: 14*(4+5x)*x^3/(1-x)^10.

a(n) = C(n+1, 4)*C(n+5, 5). - Zerinvary Lajos, May 26 2005; corrected by R. J. Mathar, Feb 10 2016

From Amiram Eldar, Feb 04 2022: (Start)

Sum_{n>=3} 1/a(n) = 290341/8820 - 10*Pi^2/3.

Sum_{n>=3} (-1)^(n+1)/a(n) = 5*Pi^2/3 - 128*log(2)/7 - 3683/980. (End)

MATHEMATICA

Table[14 * (n+1) * Binomial[n+5, 8], {n, 3, 50}] (* Amiram Eldar, Feb 04 2022 *)

LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {56, 630, 3780, 16170, 55440, 162162, 420420, 990990, 2162160, 4424420}, 30] (* Harvey P. Dale, Aug 07 2025 *)

CROSSREFS

Sequence in context: A234106 A219475 A264212 * A199914 A190535 A190604

Adjacent sequences: A027810 A027811 A027812 * A027814 A027815 A027816

KEYWORD

nonn,easy

AUTHOR

Thi Ngoc Dinh (via R. K. Guy)

STATUS

approved