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A062127 Seventh column of A046741. 9
13, 223, 1577, 7018, 23431, 64316, 153190, 327718, 644573, 1185025, 2061259, 3423422, 5467399, 8443318, 12664784, 18518842, 26476669, 37104995, 51078253, 69191458, 92373815, 121703056, 158420506, 203946878, 259898797, 328106053 (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 (7,-21,35,-35,21,-7,1).

FORMULA

G.f.: (2*x^6 + 14*x^5 + 72*x^4 + 207*x^3 + 289*x^2 + 132*x + 13)/(1-x)^7. 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) = (81*n^6 + 567*n^5 + 2205*n^4 + 4545*n^3 + 5674*n^2 + 3728*n + 1040)/80.

E.g.f.: (1040 + 16800*x + 45760*x^2 + 39240*x^3 + 13140*x^4 + 1782*x^5 + 81*x^6)*exp(x)/80. (End)

MATHEMATICA

Table[(81*n^6 +567*n^5 +2205*n^4 +4545*n^3 +5674*n^2 +3728*n +1040)/80, {n, 0, 40}] (* G. C. Greubel, Jan 31 2019 *)

LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {13, 223, 1577, 7018, 23431, 64316, 153190}, 30] (* Harvey P. Dale, Jun 07 2022 *)

PROG

(PARI) vector(40, n, n--; (81*n^6 +567*n^5 +2205*n^4 +4545*n^3 +5674*n^2 +3728*n +1040)/80) \\ G. C. Greubel, Jan 31 2019

(Magma) [(81*n^6 +567*n^5 +2205*n^4 +4545*n^3 +5674*n^2 +3728*n +1040)/80: n in [0..40]]; // G. C. Greubel, Jan 31 2019

(Sage) [(81*n^6 +567*n^5 +2205*n^4 +4545*n^3 +5674*n^2 +3728*n +1040)/80 for n in range(40)] # G. C. Greubel, Jan 31 2019

(GAP) List([0..40], n -> (81*n^6 +567*n^5 +2205*n^4 +4545*n^3 +5674*n^2 +3728*n +1040)/80); # G. C. Greubel, Jan 31 2019

CROSSREFS

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

Sequence in context: A051180 A143832 A140841 * A178559 A068120 A237602

Adjacent sequences: A062124 A062125 A062126 * A062128 A062129 A062130

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 1 12:40 EST 2022. Contains 358468 sequences. (Running on oeis4.)