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A027806
a(n) = 30*(n+1)*binomial(n+4,10).
1
210, 2640, 17820, 85800, 330330, 1081080, 3123120, 8168160, 19691100, 44341440, 94225560, 190466640, 368588220, 686439600, 1235591280, 2157381600, 3665097150, 6074125200, 9842332500, 15623407800, 24336462150, 37255818600, 56125648800, 83304936000, 121949170200
OFFSET
6,1
COMMENTS
Number of 15-subsequences of [ 1, n ] with just 4 contiguous pairs.
LINKS
Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
FORMULA
G.f.: 30*(7+4x)*x^6/(1-x)^12.
a(n) = C(n+1, 7)*C(n+4, 4). - Zerinvary Lajos, May 26 2005; corrected by R. J. Mathar, Feb 13 2016
From Amiram Eldar, Feb 03 2022: (Start)
Sum_{n>=6} 1/a(n) = 14*Pi^2/3 - 10444807/226800.
Sum_{n>=6} (-1)^n/a(n) = 7*Pi^2/3 + 3584*log(2)/45 - 2534651/32400. (End)
MATHEMATICA
Table[30 * (n+1) * Binomial[n+4, 10], {n, 6, 50}] (* Amiram Eldar, Feb 03 2022 *)
CROSSREFS
Sequence in context: A135201 A187663 A064260 * A024407 A027822 A024449
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved