A050404 Partial sums of A051878.

1, 14, 77, 280, 798, 1932, 4158, 8184, 15015, 26026, 43043, 68432, 105196, 157080, 228684, 325584, 454461, 623238, 841225, 1119272, 1469930, 1907620, 2448810, 3112200, 3918915, 4892706, 6060159, 7450912

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. A051878.

Cf. A093565 ((8, 1) Pascal, column m=6).

Programs

GAP

List([0..40], n-> (4*n+3)*Binomial(n+5,5)/3); # G. C. Greubel, Aug 30 2019

Magma

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

Maple

seq((4*n+3)*binomial(n+5,5)/3, n=0..40); # G. C. Greubel, Aug 30 2019

Mathematica

Table[(4*n+3)*Binomial[n+5,5]/3, {n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Apr 19 2011, modified by G. C. Greubel, Aug 30 2019 *)

PARI

vector(40, n, (4*n-1)*binomial(n+4,5)/3) \\ G. C. Greubel, Aug 30 2019

Sage

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

Formula

a(n) = binomial(n+5, 5)*(4*n+3)/3.

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

E.g.f.: (360 +4680*x +9000*x^2 +5400*x^3 +1275*x^4 +123*x^5 +4*x^6 )*exp(x)/360. - G. C. Greubel, Aug 30 2019

Extensions

Corrected by T. D. Noe, Nov 09 2006