A050405 Partial sums of A051879.

1, 15, 84, 308, 882, 2142, 4620, 9108, 16731, 29029, 48048, 76440, 117572, 175644, 255816, 364344, 508725, 697851, 942172, 1253868, 1647030, 2137850, 2744820, 3488940, 4393935, 5486481, 6796440, 8357104

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) = binomial(n+5, 5)*(3*n + 2)/2.

G.f.: (1+8*x)/(1-x)^7.

E.g.f.: (240 +3360*x +6600*x^2 +4000*x^3 +950*x^4 +92*x^5 +3* x^6) *exp(x)/240. - G. C. Greubel, Oct 30 2019

Maple

seq(binomial(n+5, 5)*(3*n+2)/2, n=0..40); # G. C. Greubel, Oct 30 2019

Mathematica

Accumulate[Accumulate[Table[(n+1)(n+2)(n+3)(9n+4)/24, {n, 0, 40}]]] (* Harvey P. Dale, Aug 19 2012 *)

Prog

(PARI) vector(41, n, binomial(n+4, 5)*(3*n-1)/2) \\ G. C. Greubel, Oct 30 2019
(Magma) [Binomial(n+5, 5)*(3*n+2)/2: n in [0..40]]; // G. C. Greubel, Oct 30 2019
(Sage) [binomial(n+5, 5)*(3*n+2)/2 for n in (0..40)] # G. C. Greubel, Oct 30 2019
(GAP) List([0..40], n-> Binomial(n+5, 5)*(3*n+2)/2); # G. C. Greubel, Oct 30 2019

Crossrefs

Cf. A051879.

Cf. A093644 ((9, 1) Pascal, column m=6).

Sequence in context: A252935 A247958 A108674 * A241220 A279740 A281189

Adjacent sequences: A050402 A050403 A050404 * A050406 A050407 A050408

Keyword

easy,nonn

Author

Barry E. Williams, Dec 21 1999

Extensions

Corrected by T. D. Noe, Nov 09 2006

Status

approved