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

0,2

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)*(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

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 *)

Prog

(PARI) a(n) = binomial(n+5, 5)*(7*n+6)/6; \\ Michel Marcus, Jan 09 2015
(Magma) [(7*n+6)*Binomial(n+5, 5)/6: n in [0..30]]; // G. C. Greubel, Aug 29 2019
(Sage) [(7*n+6)*binomial(n+5, 5)/6 for n in (0..30)] # G. C. Greubel, Aug 29 2019
(GAP) List([0..30], n-> (7*n+6)*Binomial(n+5, 5)/6); # G. C. Greubel, Aug 29 2019

Crossrefs

Cf. A051877.

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

Sequence in context: A146381 A085461 A081860 * A235454 A296831 A031442

Adjacent sequences: A050400 A050401 A050402 * A050404 A050405 A050406

Keyword

easy,nonn

Author

Barry E. Williams, Dec 21 1999

Extensions

Corrected by T. D. Noe, Nov 09 2006

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

Status

approved