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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 (list; graph; refs; listen; history; text; internal format)
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)*(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

Adjacent sequences:  A050403 A050404 A050405 * A050407 A050408 A050409

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, Dec 21 1999

EXTENSIONS

Corrected by T. D. Noe, Nov 09 2006

STATUS

approved

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Last modified April 14 05:25 EDT 2021. Contains 342944 sequences. (Running on oeis4.)