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A062126 Sixth column of A046741. 1
8, 114, 667, 2504, 7191, 17266, 36482, 70050, 124882, 209834, 335949, 516700, 768233, 1109610, 1563052, 2154182, 2912268, 3870466, 5066063, 6540720, 8340715, 10517186, 13126374, 16229866, 19894838, 24194298, 29207329 (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

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

G.f.: (x+2)*(2*x^4 + 8*x^3 + 36*x^2 + 31*x + 4)/(1-x)^6. 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).

From G. C. Greubel, Jan 31 2019: (Start)

a(n) = (320 + 1114*n + 1515*n^2 + 1125*n^3 + 405*n^4 + 81*n^5)/40.

E.g.f.: (320 + 4240*x + 8940*x^2 + 5580*x^3 + 1215*x^4 + 81*x^5)*exp(x)/40. (End)

MATHEMATICA

Table[(320+1114*n+1515*n^2+1125*n^3+405*n^4+81*n^5)/40, {n, 0, 40}] (* G. C. Greubel, Jan 31 2019 *)

PROG

(PARI) vector(40, n, n--; (320+1114*n+1515*n^2+1125*n^3+405*n^4 + 81*n^5)/40) \\ G. C. Greubel, Jan 31 2019

(MAGMA) [(320+1114*n+1515*n^2+1125*n^3+405*n^4+81*n^5)/40: n in [0..40]]; // G. C. Greubel, Jan 31 2019

(Sage) [(320+1114*n+1515*n^2+1125*n^3+405*n^4+81*n^5)/40 for n in range(40)] # G. C. Greubel, Jan 31 2019

(GAP) List([0..40], n -> (320+1114*n+1515*n^2+1125*n^3+405*n^4+81*n^5 )/40); # G. C. Greubel, Jan 31 2019

CROSSREFS

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

Sequence in context: A099715 A023814 A217772 * A222520 A220635 A113670

Adjacent sequences:  A062123 A062124 A062125 * A062127 A062128 A062129

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 April 17 14:32 EDT 2021. Contains 343063 sequences. (Running on oeis4.)