login
A050405
Partial sums of A051879.
5
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.
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
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Dec 21 1999
EXTENSIONS
Corrected by T. D. Noe, Nov 09 2006
STATUS
approved