A102741 a(n) = 3^4 * binomial(n+3, 4).

81, 405, 1215, 2835, 5670, 10206, 17010, 26730, 40095, 57915, 81081, 110565, 147420, 192780, 247860, 313956, 392445, 484785, 592515, 717255, 860706, 1024650, 1210950, 1421550, 1658475, 1923831, 2219805, 2548665, 2912760, 3314520, 3756456, 4241160, 4771305, 5349645

Offset: 1

Author

Zerinvary Lajos, Aug 06 2008

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A027465.

Sequences of the form 3^m*binomial(n+m-1, m): A008585 (m=1), A027468 (m=2), A134171 (m=3), this sequence (m=4), A113335 (m=5).

Programs

Magma

[3^4*Binomial(n+3,4): n in [1..30]]; // G. C. Greubel, May 17 2021

Maple

seq(binomial(n+3,4)*3^4, n=1..27);

Mathematica

With[{c=3^4},Table[c Binomial[n+3,4],{n,40}]]  (* Harvey P. Dale, Mar 12 2011 *)

Sage

[3^4*binomial(n+3,4) for n in (1..30)] # G. C. Greubel, May 17 2021

Formula

G.f.: 81*x/(1-x)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009

E.g.f.: (27/8)*x*(24 + 36*x + 12*x^2 + x^3)*exp(x). - G. C. Greubel, May 17 2021

From Amiram Eldar, Aug 28 2022: (Start)

Sum_{n>=1} 1/a(n) = 4/243.

Sum_{n>=1} (-1)^(n+1)/a(n) = 32*log(2)/81 - 64/243. (End)