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A056001 A second-order recursive sequence. 4
1, 16, 108, 480, 1650, 4752, 12012, 27456, 57915, 114400, 213928, 381888, 655044, 1085280, 1744200, 2728704, 4167669, 6229872, 9133300, 13156000, 18648630, 26048880, 35897940, 48859200, 65739375, 87512256, 115345296, 150629248 (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

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

FORMULA

a(n) = (n+1)*C(n+7, 7).

G.f.: (1+7*x)/(1-x)^9.

a(n) = A245334(n+7,7)/A000142(7). - Reinhard Zumkeller, Aug 31 2014

a(n) = A000581(n+8)+7*A000581(n+7). - R. J. Mathar, Oct 24 2014

E.g.f.: (5040 +75600*x +194040*x^2 +170520*x^3 +66150*x^4 +12642*x^5 + 1225*x^6 +57*x^7 +x^8)*exp(x)/5040. - G. C. Greubel, Aug 29 2019

MAPLE

seq((n+1)*binomial(n+7, 7), n=0..30); # G. C. Greubel, Aug 29 2019

MATHEMATICA

Table[(n+1)Binomial[n+7, 7], {n, 0, 30}] (* Vladimir Joseph Stephan Orlovsky, Apr 19 2011 *)

PROG

(Haskell)

a056001 n = (n + 1) * a007318' (n + 7) 7

-- Reinhard Zumkeller, Aug 31 2014

(PARI) vector(30, n, n*binomial(n+6, 7)) \\ G. C. Greubel, Aug 29 2019

(Magma) [(n+1)*Binomial(n+7, 7): n in [0..30]]; // G. C. Greubel, Aug 29 2019

(Sage) [(n+1)*binomial(n+7, 7) for n in (0..30)] # G. C. Greubel, Aug 29 2019

(GAP) List([0..30], n-> (n+1)*Binomial(n+7, 7)); # G. C. Greubel, Aug 29 2019

CROSSREFS

Cf. A052226.

Cf. A093565 ((8, 1) Pascal, column m=8). Partial sums of A052226.

Cf. A007318, A000142, A245334.

Sequence in context: A224160 A224411 A260357 * A163725 A269188 A165558

Adjacent sequences: A055998 A055999 A056000 * A056002 A056003 A056004

KEYWORD

nonn,easy

AUTHOR

Barry E. Williams, Jun 18 2000

EXTENSIONS

Mathematica code corrected by Bruno Berselli, Jan 23 2015

STATUS

approved

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Last modified December 5 15:27 EST 2022. Contains 358588 sequences. (Running on oeis4.)