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A052254 Partial sums of A050406. 3
1, 17, 108, 444, 1410, 3762, 8844, 18876, 37323, 69355, 122408, 206856, 336804, 531012, 813960, 1217064, 1780053, 2552517, 3595636, 4984100, 6808230, 9176310, 12217140, 16082820, 20951775 (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.

Murray R. Spiegel, Calculus of Finite Differences and Difference Equations, "Schaum's Outline Series", McGraw-Hill, 1971, pp. 10-20, 79-94.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1)

FORMULA

a(n) = (10*n + 7)*binomial(n+6, 6)/7.

G.f.: (1+9*x)/(1-x)^8.

From G. C. Greubel, Jan 19 2020: (Start)

a(n) = 10*binomial(n+7, 7) - 9*binomial(n+6, 6).

E.g.f.: (7! + 80640*x + 189000*x^2 + 142800*x^3 + 45150*x^4 + 6552*x^5 + 427*x^6 + 10*x^7)*exp(x)/7!. (End)

MAPLE

seq( (10*n+7)*binomial(n+6, 6)/7, n=0..30); # G. C. Greubel, Jan 19 2020

MATHEMATICA

Table[10*Binomial[n+7, 7] -9*Binomial[n+6, 6], {n, 0, 30}] (* G. C. Greubel, Jan 19 2020 *)

Rest[Nest[Accumulate[#]&, Table[n(n+1)(10n-7)/6, {n, 0, 50}], 4]] (* Harvey P. Dale, Aug 03 2020 *)

PROG

(PARI) vector(31, n, (10*n-3)*binomial(n+5, 6)/7) \\ G. C. Greubel, Jan 19 2020

(MAGMA) [(10*n+7)*Binomial(n+6, 6)/7: n in [0..30]]; // G. C. Greubel, Jan 19 2020

(Sage) [(10*n+7)*binomial(n+6, 6)/7 for n in (0..30)] # G. C. Greubel, Jan 19 2020

(GAP) List([0..30], n-> (10*n+7)*Binomial(n+6, 6)/7 ); # G. C. Greubel, Jan 19 2020

CROSSREFS

Cf. A050406.

Cf. A093645 ((10, 1) Pascal, column m=7).

Sequence in context: A159031 A080441 A135400 * A156851 A141921 A013308

Adjacent sequences:  A052251 A052252 A052253 * A052255 A052256 A052257

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, Feb 03 2000

STATUS

approved

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Last modified April 14 04:41 EDT 2021. Contains 342941 sequences. (Running on oeis4.)