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

0,2

References

Albert 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

Sum_{n>=0} 1/a(n) = -707966/115005 - 1835008*Pi/115005 - 1835008*sqrt(2)*Pi/115005 + 3670016*sqrt(2)*log(sqrt(2)+1)/115005 + 14680064*log(2)/115005. - Amiram Eldar, Sep 27 2025

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
(SageMath) [(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: A394960 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