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A052226 Partial sums of A050404. 3
1, 15, 92, 372, 1170, 3102, 7260, 15444, 30459, 56485, 99528, 167960, 273156, 430236, 658920, 984504, 1438965, 2062203, 2903428, 4022700, 5492630, 7400250, 9849060, 12961260, 16880175, 21772881, 27833040, 35283952, 44381832, 55419320, 68729232, 84688560, 103722729, 126310119 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

Murray R. Spiegel, Calculus of Finite Differences and Difference Equations, "Schaum's Outline Series", McGraw-Hill, 1971, pp. 10-20, 79-94.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

FORMULA

a(n) = (8*n+7)*C(n+6, 6)/7.

G.f.: (1+7*x)/(1-x)^8.

E.g.f.: (5040 +70560*x +158760*x^2 +117600*x^3 +36750*x^4 +5292*x^5 +343*x^6 +8*x^7)*exp(x)/5040. - G. C. Greubel, Aug 29 2019

MAPLE

seq((8*n+7)*Binomial(n+6, 6)/7, n=0..40); # G. C. Greubel, Aug 29 2019

MATHEMATICA

Table[(8*n+7)*Binomial[n+6, 6]/7, {n, 0, 40}] (* G. C. Greubel, Aug 29 2019 *)

LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {1, 15, 92, 372, 1170, 3102, 7260, 15444}, 40] (* Harvey P. Dale, Aug 12 2021 *)

PROG

(PARI) vector(40, n, (8*n-1)*binomial(n+5, 6)/7) \\ G. C. Greubel, Aug 29 2019

(Magma) [(8*n+7)*Binomial(n+6, 6)/7: n in [0..40]]; // G. C. Greubel, Aug 29 2019

(Sage) [(8*n+7)*binomial(n+6, 6)/7 for n in (0..40)] # G. C. Greubel, Aug 29 2019

(GAP) List([0..40], n-> (8*n+7)*Binomial(n+6, 6)/7); # G. C. Greubel, Aug 29 2019

CROSSREFS

Cf. A050404.

Cf. A093565 ((8, 1) Pascal, column m=7).

Sequence in context: A180248 A329759 A041428 * A108684 A125325 A126483

Adjacent sequences: A052223 A052224 A052225 * A052227 A052228 A052229

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, Jan 29 2000

EXTENSIONS

Terms a(25) onward added by G. C. Greubel, Aug 29 2019

STATUS

approved

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Last modified December 5 12:42 EST 2022. Contains 358586 sequences. (Running on oeis4.)