|
|
A055843
|
|
Expansion of (1+3*x)/(1-x)^10.
|
|
3
|
|
|
1, 13, 85, 385, 1375, 4147, 11011, 26455, 58630, 121550, 238238, 445094, 797810, 1379210, 2309450, 3759074, 5965487, 9253475, 14060475, 20967375, 30735705, 44352165, 63081525, 88529025, 122713500, 168152556, 227961228, 305965660, 406833460, 536222500, 700950052
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
|
|
REFERENCES
|
Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
|
|
LINKS
|
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
|
|
FORMULA
|
a(n) = (4*n+9)*binomial(n+8, 8)/9.
G.f.: (1+3*x)/(1-x)^10.
a(n) = 4*binomial(n+9,9) - 3*binomial(n+8,8). - G. C. Greubel, Jan 21 2020
Sum_{n>=0} 1/a(n) = 9437184*Pi/24035 + 56623104*log(2)/24035 - 482087736/168245. - Amiram Eldar, Feb 17 2023
|
|
MAPLE
|
seq( (4*n+9)*binomial(n+8, 8)/9, n=0..30); # G. C. Greubel, Jan 21 2020
|
|
MATHEMATICA
|
Table[4*Binomial[n+9, 9] - 3*Binomial[n+8, 8], {n, 0, 30}] (* G. C. Greubel, Jan 21 2020 *)
|
|
PROG
|
(PARI) vector(31, n, (4*n+5)*binomial(n+7, 8)/9) \\ G. C. Greubel, Jan 21 2020
(Magma) [(4*n+9)*Binomial(n+8, 8)/9: n in [0..30]]; // G. C. Greubel, Jan 21 2020
(Sage) [(4*n+9)*binomial(n+8, 8)/9 for n in (0..30)] # G. C. Greubel, Jan 21 2020
(GAP) List([0..30], n-> (4*n+9)*Binomial(n+8, 8)/9 ); # G. C. Greubel, Jan 21 2020
|
|
CROSSREFS
|
Cf. A093561 ((4, 1) Pascal, column m=9).
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|