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)
2
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 (list; graph; refs; listen; history; internal format)
OFFSET

3,1

REFERENCES

L. Carlitz et al., Permutations and sequences with repetions 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

S. 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.

S. 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 (deutsch(AT)duke.poly.edu), Jan 27 2005

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 S. Plouffe in his 1992 dissertation.]

CROSSREFS

Sequence in context: A089207 A027777 A073773 * A005553 A055344 A059021

Adjacent sequences:  A001916 A001917 A001918 * A001920 A001921 A001922

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 27 2005

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 February 14 04:19 EST 2012. Contains 205570 sequences.