A027804 - OEIS

A027804

a(n) = 14*(n+1)*binomial(n+4,8).

70, 756, 4410, 18480, 62370, 180180, 462462, 1081080, 2342340, 4764760, 9189180, 16930368, 29980860, 51279480, 85058820, 137287920, 216228474, 333125100, 503052550, 745945200, 1087836750, 1562340780, 2212405650, 3092380200, 4270429800, 5831345520, 7879792536

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OFFSET

4,1

COMMENTS

Number of 13-subsequences of [ 1, n ] with just 4 contiguous pairs.

LINKS

Table of n, a(n) for n=4..30.

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

FORMULA

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

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

From Amiram Eldar, Feb 04 2022: (Start)

Sum_{n>=4} 1/a(n) = 10*Pi^2/3 - 145013/4410.

Sum_{n>=4} (-1)^n/a(n) = 5*Pi^2/3 + 128*log(2)/7 - 42793/1470. (End)

MATHEMATICA

Table[14 * (n+1) * Binomial[n+4, 8], {n, 4, 50}] (* Amiram Eldar, Feb 04 2022 *)

LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {70, 756, 4410, 18480, 62370, 180180, 462462, 1081080, 2342340, 4764760}, 30] (* Harvey P. Dale, Aug 26 2024 *)

CROSSREFS

Sequence in context: A199829 A271495 A232587 * A212236 A177298 A230897

Adjacent sequences: A027801 A027802 A027803 * A027805 A027806 A027807

KEYWORD

nonn,easy

AUTHOR

Thi Ngoc Dinh (via R. K. Guy)

STATUS

approved