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A062125 Fifth column of A046741. 1
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

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

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

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

a(n) = (40 + 126*n + 165*n^2 + 90*n^3 + 27*n^4)/8.

E.g.f.: (40 + 408*x + 624*x^2 + 252*x^3 + 27*x^4)*exp(x)/8. (End)

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 *)

Table[(40+126*n+165*n^2+90*n^3+27*n^4)/8, {n, 0, 40}] (* G. C. Greubel, Jan 31 2019 *)

PROG

(PARI) vector(40, n, n--; (40+126*n+165*n^2+90*n^3+27*n^4)/8) \\ G. C. Greubel, Jan 31 2019

(Magma) [(40+126*n+165*n^2+90*n^3+27*n^4)/8: n in [0..40]]; // G. C. Greubel, Jan 31 2019

(Sage) [(40+126*n+165*n^2+90*n^3+27*n^4)/8 for n in range(40)] # G. C. Greubel, Jan 31 2019

(GAP) List([0..40], n -> (40+126*n+165*n^2+90*n^3+27*n^4)/8); # G. C. Greubel, Jan 31 2019

CROSSREFS

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

Sequence in context: A174514 A041995 A288543 * 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 6 10:23 EST 2022. Contains 358630 sequences. (Running on oeis4.)