login
This site is supported by donations to The OEIS Foundation.
Logo

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A001919 Eighth column of quadrinomial coefficients.
(Formerly M4234 N1769)
4
6, 40, 155, 456, 1128, 2472, 4950, 9240, 16302, 27456, 44473, 69680, 106080, 157488, 228684, 325584, 455430, 627000, 850839, 1139512, 1507880, 1973400, 2556450, 3280680, 4173390, 5265936, 6594165, 8198880, 10126336, 12428768, 15164952, 18400800, 22209990 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

REFERENCES

L. Carlitz et al., Permutations and sequences with repetitions by number of increases, J. Combin. Theory, 1 (1966), 350-374.

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 78.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n = 3..1000

_Simon Plouffe_, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

_Simon Plouffe_, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

FORMULA

a(n) = A008287(n, 7) = binomial(n+2, 5)*(n^2+21*n+180 )/42, n >= 3.

G.f.: (x^3)*(6-8*x+3*x^2 )/(1-x)^8. Numerator polynomial is N4(7, x) from array A063421.

a(n) = n(n^2-1)(n^2-4)(n^2+21n+180)/5040. - Emeric Deutsch, Jan 27 2005

a(n) = 6*C(n,3) + 16*C(n,4) + 15*C(n,5) + 6*C(n,6) + C(n,7) (see comment in A071675). - Vladimir Shevelev and Peter Moses, Jun 22 2012

a(3)=6, a(4)=40, a(5)=155, a(6)=456, a(7)=1128, a(8)=2472, a(9)=4950, a(10)=9240, a(n)=8*a(n-1)-28*a(n-2)+56*a(n-3)-70*a(n-4)+56*a(n-5)- 28*a(n-6)+ 8*a(n-7)-a(n-8). - Harvey P. Dale, Mar 27 2013

MAPLE

seq(n*(n^2-1)*(n^2-4)*(n^2+21*n+180)/5040, n=3..34); (Deutsch)

A001919:=(3*z**2-8*z+6)/(z-1)**8; [Conjectured by Simon Plouffe in his 1992 dissertation.]

MATHEMATICA

Table[n*(n^2 - 1)*(n^2 - 4)*(n^2 + 21*n + 180)/5040, {n, 3, 50}] (* T. D. Noe, Aug 17 2012 *)

LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {6, 40, 155, 456, 1128, 2472, 4950, 9240}, 40] (* Harvey P. Dale, Mar 27 2013 *)

CROSSREFS

Sequence in context: A089207 A027777 A073773 * A005553 A055344 A210424

Adjacent sequences:  A001916 A001917 A001918 * A001920 A001921 A001922

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Emeric Deutsch, Jan 27 2005

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified May 21 18:02 EDT 2013. Contains 225504 sequences.