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A050406
Partial sums of A051880.
3
1, 16, 91, 336, 966, 2352, 5082, 10032, 18447, 32032, 53053, 84448, 129948, 194208, 282948, 403104, 562989, 772464, 1043119, 1388464, 1824130, 2368080, 3040830, 3865680, 4868955, 6080256, 7532721, 9263296
OFFSET
0,2
REFERENCES
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
FORMULA
a(n) = C(n+5, 5)*(5*n + 3)/3.
G.f.: (1+9*x)/(1-x)^7.
E.g.f.: (360 +5400*x +10800*x^2 +6600*x^3 +1575*x^4 +153*x^5 +5*x^6) *exp(x)/360. - G. C. Greubel, Oct 30 2019
MAPLE
seq(binomial(n+5, 5)*(5*n+3)/3, n=0..40); # G. C. Greubel, Oct 30 2019
MATHEMATICA
Nest[Accumulate[#]&, Table[n(n+1)(10n-7)/6, {n, 0, 50}], 3] (* Harvey P. Dale, Nov 13 2013 *)
PROG
(PARI) vector(41, n, binomial(n+4, 5)*(5*n-2)/3) \\ G. C. Greubel, Oct 30 2019
(Magma) [Binomial(n+5, 5)*(5*n+3)/3: n in [0..40]]; // G. C. Greubel, Oct 30 2019
(Sage) [binomial(n+5, 5)*(5*n+3)/3 for n in (0..40)] # G. C. Greubel, Oct 30 2019
(GAP) List([0..40], n-> Binomial(n+5, 5)*(5*n+3)/3); # G. C. Greubel, Oct 30 2019
CROSSREFS
Cf. A051880.
Cf. A093645 ((10, 1) Pascal, column m=6).
Sequence in context: A055856 A195591 A240292 * A047674 A153029 A170920
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Dec 21 1999
EXTENSIONS
Corrected by T. D. Noe, Nov 09 2006
STATUS
approved