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 A007662 Quadruple factorial numbers n!!!!: a(n) = n*a(n-4). (Formerly M0534) 63
 1, 1, 2, 3, 4, 5, 12, 21, 32, 45, 120, 231, 384, 585, 1680, 3465, 6144, 9945, 30240, 65835, 122880, 208845, 665280, 1514205, 2949120, 5221125, 17297280, 40883535, 82575360, 151412625, 518918400, 1267389585, 2642411520, 4996616625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). J. Spanier and K. B. Oldham, An Atlas of Functions, Hemisphere, NY, 1987, p. 23. LINKS Klaus Brockhaus, Table of n, a(n) for n = 0..500 Eric Weisstein's World of Mathematics, Multifactorial. FORMULA a(n) ~ c * n^(n/4+1/2)/exp(n/4), where c = sqrt(Pi/2) if n=4*k, c = 2*sqrt(Pi)/Gamma(1/4) if n=4*k+1, c = sqrt(2) if n=4*k+2, c = sqrt(Pi)/Gamma(3/4) if n=4*k+3. - Vaclav Kotesovec, Jul 29 2013 Sum_{n>=0} 1/a(n) = A288091. - Amiram Eldar, Nov 10 2020 MATHEMATICA NFactorialM[n_Integer, m_Integer] := Block[{k = n, p = Max[1, n]}, While[k > m, k -= m; p *= k]; p]; Table[ NFactorialM[n, 4], {n, 0, 34}] (* Robert G. Wilson v *) With[{k = 4}, Table[With[{q = Quotient[n + k - 1, k]}, k^q q! Binomial[n/k, q]], {n, 0, 34}]] (* Jan Mangaldan, Mar 21 2013 *) PROG (MAGMA) I:=[ 1, 1, 2, 3 ]; [ n le 4 select I[n] else (n-1)*Self(n-4): n in [1..36] ]; // Klaus Brockhaus, Jun 23 2011 (MAGMA) A007662:=func< n | n eq 0 select 1 else &*[ k: k in [1..n] | k mod 4 eq n mod 4 ] >; [ A007662(n): n in [0..35] ]; // Klaus Brockhaus, Jun 23 2011 (PARI) a(n)=if(n<6, max(n, 1), n*a(n-4)) \\ Charles R Greathouse IV, Jun 23 2011 CROSSREFS Cf. A047053, A007696, A001813, A008545, A000142, A006882, A007661, A288091. Sequence in context: A333390 A117577 A109849 * A069469 A175807 A165303 Adjacent sequences:  A007659 A007660 A007661 * A007663 A007664 A007665 KEYWORD nonn AUTHOR STATUS approved

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Last modified November 29 17:53 EST 2020. Contains 338769 sequences. (Running on oeis4.)