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A062125 Fifth column of A046741. 0
5, 56, 263, 815, 1982, 4115, 7646, 13088, 21035, 32162, 47225, 67061, 92588, 124805, 164792, 213710, 272801, 343388, 426875, 524747, 638570, 769991, 920738, 1092620, 1287527, 1507430, 1754381, 2030513, 2338040, 2679257, 3056540 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983,(2.3.14).

LINKS

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

FORMULA

G.f.: (5+33*x^2+10*x^3+31*x+2*x^4)/(1-x)^5. Generally, g.f. for k-th column of A046741 is coefficient of y^k in expansion of (1-y)/((1-y-y^2)*(1-y)-(1+y)*x).

a(0)=5, a(1)=56, a(2)=263, a(3)=815, a(4)=1982, a(n)=5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5) [From Harvey P. Dale, Dec 21 2011]

MATHEMATICA

LinearRecurrence[{5, -10, 10, -5, 1}, {5, 56, 263, 815, 1982}, 31] (* or *) CoefficientList[Series[(5+33x^2+10x^3+31x+2x^4)/(1-x)^5, {x, 0, 30}], x] (* Harvey P. Dale, Dec 21 2011 *)

CROSSREFS

Cf. dumbbells: A002940, A002941, A002889, A046741, A055608, A062123-A062127.

Sequence in context: A072318 A174514 A041995 * A030060 A247710 A247774

Adjacent sequences:  A062122 A062123 A062124 * A062126 A062127 A062128

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Jun 04 2001

EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), Jun 06 2001

STATUS

approved

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Last modified December 11 03:18 EST 2016. Contains 279034 sequences.