A050403 Partial sums of A051877.

1, 13, 70, 252, 714, 1722, 3696, 7260, 13299, 23023, 38038, 60424, 92820, 138516, 201552, 286824, 400197, 548625, 740278, 984676, 1292830, 1677390, 2152800, 2735460, 3443895, 4298931, 5323878, 6544720, 7990312, 9692584, 11686752, 14011536, 16709385, 19826709, 23414118, 27526668

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. A051877.

Cf. A093564 ((7, 1) Pascal, column m=6).

Programs

GAP

List([0..30], n-> (7*n+6)*Binomial(n+5, 5)/6); # G. C. Greubel, Aug 29 2019

Magma

[(7*n+6)*Binomial(n+5, 5)/6: n in [0..30]]; // G. C. Greubel, Aug 29 2019

Maple

Seq((7*n+6)*binomial(n+5, 5)/6, n=0..30); # G. C. Greubel, Aug 29 2019

Mathematica

Table[(7*n+6)*Binomial[n+5, 5]/6, {n,0,30}] (* G. C. Greubel, Aug 29 2019 *)

PARI

a(n) = binomial(n+5,5)*(7*n+6)/6; \\ Michel Marcus, Jan 09 2015

Sage

[(7*n+6)*binomial(n+5, 5)/6 for n in (0..30)] # G. C. Greubel, Aug 29 2019

Formula

a(n) = C(n+5, 5)*(7*n+6)/6.

G.f.: (1+6*x)/(1-x)^7.

E.g.f.: (5! +8640*x +16200*x^2 +9600*x^3 +2250*x^4 +216*x^5 +7*x^6 )*exp(x)/5!. - G. C. Greubel, Aug 29 2019

Extensions

Corrected by T. D. Noe, Nov 09 2006

Terms a(28) onward added by G. C. Greubel, Aug 29 2019