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

0,2

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).

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

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 *)

Prog

(PARI) vector(41, n, binomial(n+4, 5)*(5*n-2)/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
(Sage) [binomial(n+5, 5)*(5*n+3)/3 for n in (0..40)] # G. C. Greubel, Oct 30 2019
(GAP) List([0..40], n-> Binomial(n+5, 5)*(5*n+3)/3); # G. C. Greubel, Oct 30 2019

Crossrefs

Cf. A051880.

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

Sequence in context: A055856 A195591 A240292 * A047674 A153029 A170920

Adjacent sequences: A050403 A050404 A050405 * A050407 A050408 A050409

Keyword

easy,nonn

Author

Barry E. Williams, Dec 21 1999

Extensions

Corrected by T. D. Noe, Nov 09 2006

Status

approved