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A270272 a(n) = binomial(n+3,n)^3. 1
1, 64, 1000, 8000, 42875, 175616, 592704, 1728000, 4492125, 10648000, 23393656, 48228544, 94196375, 175616000, 314432000, 543338496, 909853209, 1481544000, 2352637000, 3652264000, 5554637011, 8291469824, 12167000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..22.

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

FORMULA

G.f.: 3F2(4,4,4;1,1;z).

G.f.: (1+54x+405x^2+760x^3+405x^4+54x^5+x^6)/(x-1)^10.

a(n) = (6+11n+6n^2+n^3)^3/216.

a(n) = A000292(n+1)^3.

Sum_{n>=0} 1/a(n) = 783/4 - 162*zeta(3). - Jaume Oliver Lafont, Jul 17 2017

MAPLE

A270272:=n->binomial(n+3, n)^3: seq(A270272(n), n=0..50); # Wesley Ivan Hurt, Jul 17 2017

MATHEMATICA

Table[Binomial[n+3, n]^3, {n, 0, 30}]

PROG

(PARI) a(n) = binomial(n+3, n)^3; \\ Michel Marcus, Jul 17 2017

CROSSREFS

Cf. A000578, A000292, A001249.

Sequence in context: A016959 A224392 A224025 * A297612 A000768 A230972

Adjacent sequences:  A270269 A270270 A270271 * A270273 A270274 A270275

KEYWORD

nonn,easy

AUTHOR

Benedict W. J. Irwin, Mar 14 2016

STATUS

approved

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Last modified November 18 22:39 EST 2019. Contains 329305 sequences. (Running on oeis4.)