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 A034323 a(n) = n-th quintic factorial number divided by 2. 12
 1, 7, 84, 1428, 31416, 848232, 27143424, 1004306688, 42180880896, 1982501402112, 103090072909824, 5876134155859968, 364320317663318016, 24409461283442307072, 1757481212407846109184, 135326053355404150407168, 11096736375143140333387776, 965416064637453209004736512 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Robert Israel, Table of n, a(n) for n = 1..355 J.-C. Novelli and J.-Y. Thibon, Hopf Algebras of m-permutations,(m+1)-ary trees, and m-parking functions, arXiv:1403.5962 [math.CO], 2014-2020. FORMULA 2*a(n) = (5*n-3)(!^5) = Product_{j=1..n} (5*j-3). E.g.f.: (-1 + (1-5*x)^(-2/5))/2, with a(0) = 0. a(n) ~ sqrt(2*Pi) * 5/(2*Gamma(2/5)) * n^(9/10) * (5*n/e)^n * (1 + (109/300)/n - ...). - Joe Keane (jgk(AT)jgk.org), Nov 24 2001 D-finite with recurrence a(n) = (5*n-3)*a(n-1). - Robert Israel, Feb 10 2019 From Amiram Eldar, Dec 19 2022: (Start) a(n) = A047055(n)/2. Sum_{n>=1} 1/a(n) = 2*(e/5^3)^(1/5)*(Gamma(2/5) - Gamma(2/5, 1/5)). (End) MAPLE f:= gfun:-rectoproc({a(n)=(5*n-3)*a(n-1), a(1)=1}, a(n), remember): map(f, [\$1..40]); # Robert Israel, Feb 10 2019 MATHEMATICA Table[Product[5j-3, {j, n}]/2, {n, 20}] (* Harvey P. Dale, Nov 25 2013 *) PROG (PARI) vector(20, n, prod(j=1, n, 5*j-3)/2) \\ G. C. Greubel, Feb 10 2019 (Magma) [(&*[5*j-3: j in [1..n]])/2: n in [1..20]]; // G. C. Greubel, Feb 10 2019 (Sage) [product(5*j-3 for j in (1..n))/2 for n in (1..20)] # G. C. Greubel, Feb 10 2019 (GAP) a:=[1];; for n in [2..20] do a[n]:=(5*n-3)*a[n-1]; od; a; # G. C. Greubel, Feb 10 2019 CROSSREFS Cf. A008548, A034300, A034301, A034325, A047055. Sequence in context: A346582 A234510 A341966 * A172455 A258174 A254569 Adjacent sequences: A034320 A034321 A034322 * A034324 A034325 A034326 KEYWORD easy,nonn AUTHOR STATUS approved

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Last modified March 24 10:42 EDT 2023. Contains 361479 sequences. (Running on oeis4.)