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A203310 a(n) = A203309(n+1)/A203309(n). 3
2, 15, 252, 7560, 356400, 24324300, 2270268000, 277880803200, 43197833952000, 8315583035760000, 1942008468966720000, 540988073497872000000, 177227692877902867200000, 67457290601651778828000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..14.

FORMULA

a(n) ~ sqrt(Pi) * 2^(n+3) * n^(2*n + 1/2) / exp(2*n). - Vaclav Kotesovec, Jan 25 2019

MATHEMATICA

f[j_] := j (j + 1)/2; z = 15;

v[n_] := Product[Product[f[k] - f[j], {j, 1, k - 1}], {k, 2, n}]

Table[v[n], {n, 1, z}]   (* A203309 *)

Table[v[n + 1]/v[n], {n, 1, z - 1}]  (* A203310 *)

PROG

(Python)

from operator import mul

def f(n): return n*(n + 1)/2

def v(n): return 1 if n==1 else reduce(mul, [reduce(mul, [f(k) - f(j) for j in range(1, k)]) for k in range(2, n + 1)])

print [v(n + 1)/v(n) for n in range(1, 15)] # Indranil Ghosh, Jul 24 2017

CROSSREFS

Cf. A203306, A203309.

Sequence in context: A156750 A292798 A221100 * A102555 A264907 A195737

Adjacent sequences:  A203307 A203308 A203309 * A203311 A203312 A203313

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 01 2012

EXTENSIONS

Name corrected by Vaclav Kotesovec, Jan 25 2019

STATUS

approved

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Last modified May 28 21:37 EDT 2020. Contains 334690 sequences. (Running on oeis4.)