A052226 Partial sums of A050404.

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

Offset: 0

Author

Barry E. Williams, Jan 29 2000

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A050404.

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

Programs

GAP

List([0..40], n-> (8*n+7)*Binomial(n+6, 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

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 *)

PARI

vector(40, n, (8*n-1)*binomial(n+5, 6)/7) \\ 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

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

Extensions

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