A027815 a(n) = 42*(n+1) * binomial(n+5,10).

252, 3234, 22176, 108108, 420420, 1387386, 4036032, 10618608, 25729704, 58198140, 124156032, 251839224, 488864376, 912964668, 1647455040, 2883046320, 4908043140, 8149451310, 13228094880, 21031510500, 32809156380, 50295355110, 75866394240, 112739346720

Offset

5,1

Comments

Number of 16-subsequences of [ 1, n ] with just 5 contiguous pairs.

Links

T. D. Noe, Table of n, a(n) for n = 5..1000

Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Formula

G.f.: 42*x^5*(6 + 5*x)/(1-x)^12.

a(n) = C(n+1, 6)*C(n+5, 5). - Zerinvary Lajos, May 26 2005; corrected by R. J. Mathar, Feb 10 2016

E.g.f.: (42/10!)*x^5*(181440 + 206640*x + 82800*x^2 + 15300*x^3 + 1400*x^4 + 61*x^5 + x^6))*exp(x). - G. C. Greubel, Feb 09 2020

From Amiram Eldar, Feb 03 2022: (Start)

Sum_{n>=5} 1/a(n) = 10446907/211680 - 5*Pi^2.

Sum_{n>=5} (-1)^(n+1)/a(n) = 5*Pi^2/2 + 512*log(2)/21 - 8799517/211680. (End)

Maple

seq( 42*(n+1)*binomial(n+5, 10), n=5..30); # G. C. Greubel, Feb 09 2020

Mathematica

Table[42(n+1)Binomial[n+5, 10], {n, 5, 30}] (* Harvey P. Dale, Feb 09 2019 *)

Prog

(PARI) vector(26, n, my(m=n+4); binomial(m+1, 6)*binomial(m+5, 5)) \\ G. C. Greubel, Feb 09 2020
(Magma) [Binomial(n+1, 6)*Binomial(n+5, 5): n in [5..30]]; // G. C. Greubel, Feb 09 2020
(Sage) [42*(n+1)*binomial(n+5, 10) for n in (5..30)] # G. C. Greubel, Feb 09 2020

Crossrefs

Sequence in context: A117281 A152466 A004535 * A271496 A218418 A184498

Adjacent sequences: A027812 A027813 A027814 * A027816 A027817 A027818

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved