A306290 a(n) = 1/(Integral_{x=0..1} (x^3 - x^4)^n dx).

1, 20, 252, 2860, 30940, 325584, 3364900, 34337160, 347103900, 3483301360, 34754081648, 345120260940, 3413758188932, 33655718658800, 330869721936600, 3244839440755920, 31754250910172700, 310165459118369712, 3024542552887591120, 29449493278116018800, 286360607519186119920

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = 1/Beta(3*n+1,n+1) = (4*n+1)!/(n! * (3*n)!).

Mathematica

Table[1/Beta[3*n+1, n+1], {n, 0, 20}]

Prog

(PARI) vector(20, n, n--; (4*n+1)!/(n!*(3*n)!))
(Magma) [Factorial(4*n+1)/(Factorial(n)*Factorial(3*n)): n in [0..20]];
(Sage) [1/beta(3*n+1, n+1) for n in range(20)]
(GAP) List([0..30], n -> Factorial(4*n+1)/(Factorial(n)*Factorial(3*n)));

Crossrefs

Cf. A002457, A090816, A090957, A090969.

Sequence in context: A081143 A218101 A241228 * A075469 A028032 A348055

Adjacent sequences: A306287 A306288 A306289 * A306291 A306292 A306293

Keyword

nonn,easy

Author

G. C. Greubel, Feb 03 2019

Status

approved