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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

N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein

STATUS

approved

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