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A081895 Second binomial transform of binomial(n+3, 3). 3
1, 6, 30, 136, 579, 2358, 9288, 35640, 133893, 494262, 1797714, 6456024, 22930695, 80660934, 281309436, 973599912, 3346483977, 11431295910, 38828142342, 131206405608, 441271936971, 1477621745046, 4927988620080, 16373939547096 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A049612.

2nd binomial transform of binomial(n+3, 3), A000292.

3rd binomial transform of (1,3,3,1,0,0,0,0,...).

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (12,-54,108,-81)

FORMULA

a(n) = 3^n*(n^3 + 24*n^2 + 137*n + 162)/162.

G.f.: (1 - 2*x)^3/(1 - 3*x)^4.

E.g.f.: (6 + 18*x + 9*x^2 + x^3)*exp(3*x)/6. - G. C. Greubel, Oct 18 2018

MATHEMATICA

LinearRecurrence[{12, -54, 108, -81}, {1, 6, 30, 136}, 50] (* G. C. Greubel, Oct 18 2018 *)

PROG

(PARI) x='x+O('x^30); Vec((1-2*x)^3/(1-3*x)^4) \\ G. C. Greubel, Oct 18 2018

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-2*x)^3/(1-3*x)^4)); // G. C. Greubel, Oct 18 2018

CROSSREFS

Cf. A081896.

Sequence in context: A036068 A162743 A224290 * A030280 A034545 A002920

Adjacent sequences:  A081892 A081893 A081894 * A081896 A081897 A081898

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Mar 30 2003

STATUS

approved

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Last modified May 22 00:25 EDT 2019. Contains 323472 sequences. (Running on oeis4.)