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A113335
a(n) = 3^5 * binomial(n+4, 5).
3
243, 1458, 5103, 13608, 30618, 61236, 112266, 192456, 312741, 486486, 729729, 1061424, 1503684, 2082024, 2825604, 3767472, 4944807, 6399162, 8176707, 10328472, 12910590, 15984540, 19617390, 23882040, 28857465, 34628958, 41288373, 48934368, 57672648, 67616208
OFFSET
1,1
FORMULA
a(n) = 3^5 * binomial(n+4, 5), n >= 1.
From G. C. Greubel, May 17 2021: (Start)
G.f.: 243*x/(1-x)^6.
E.g.f.: (81/40)*x*(120 + 240*x + 120*x^2 + 20*x^3 + x^4)*exp(x). (End)
From Amiram Eldar, Aug 29 2022: (Start)
Sum_{n>=1} 1/a(n) = 5/972.
Sum_{n>=1} (-1)^(n+1)/a(n) = 80*log(2)/243 - 655/2916. (End)
MAPLE
seq(binomial(n+4, 5)*3^5, n=1..27);
MATHEMATICA
With[{c=3^5}, Table[c Binomial[n+4, 5], {n, 30}]] (* Harvey P. Dale, Apr 11 2011 *)
PROG
(Magma) [3^5*Binomial(n+4, 5): n in [1..30]]; // G. C. Greubel, May 17 2021
(Sage) [3^5*binomial(n+4, 5) for n in (1..30)] # G. C. Greubel, May 17 2021
CROSSREFS
Cf. A027465.
Sequences of the form 3^m*binomial(n+m-1, m): A008585 (m=1), A027468 (m=2), A134171 (m=3), A102741 (m=4), this sequence (m=5).
Sequence in context: A235540 A219132 A232285 * A217968 A233158 A100627
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Aug 06 2008
STATUS
approved