A050406 Partial sums of A051880.

1, 16, 91, 336, 966, 2352, 5082, 10032, 18447, 32032, 53053, 84448, 129948, 194208, 282948, 403104, 562989, 772464, 1043119, 1388464, 1824130, 2368080, 3040830, 3865680, 4868955, 6080256, 7532721, 9263296

Offset: 0

Author

Barry E. Williams, Dec 21 1999

Keywords

• easy
• nonn

References

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

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).

Crossrefs

Cf. A051880.

Cf. A093645 ((10, 1) Pascal, column m=6).

Programs

GAP

List([0..40], n-> Binomial(n+5,5)*(5*n+3)/3); # G. C. Greubel, Oct 30 2019

Magma

[Binomial(n+5,5)*(5*n+3)/3: n in [0..40]]; // G. C. Greubel, Oct 30 2019

Maple

seq(binomial(n+5,5)*(5*n+3)/3, n=0..40); # G. C. Greubel, Oct 30 2019

Mathematica

Nest[Accumulate[#]&,Table[n(n+1)(10n-7)/6,{n,0,50}],3] (* Harvey P. Dale, Nov 13 2013 *)

PARI

vector(41, n, binomial(n+4,5)*(5*n-2)/3) \\ G. C. Greubel, Oct 30 2019

Sage

[binomial(n+5,5)*(5*n+3)/3 for n in (0..40)] # G. C. Greubel, Oct 30 2019

Formula

a(n) = C(n+5, 5)*(5*n + 3)/3.

G.f.: (1+9*x)/(1-x)^7.

E.g.f.: (360 +5400*x +10800*x^2 +6600*x^3 +1575*x^4 +153*x^5 +5*x^6) *exp(x)/360. - G. C. Greubel, Oct 30 2019

Extensions

Corrected by T. D. Noe, Nov 09 2006