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A038208 Triangle whose (i,j)-th entry is binomial(i,j)*2^i. 15
1, 2, 2, 4, 8, 4, 8, 24, 24, 8, 16, 64, 96, 64, 16, 32, 160, 320, 320, 160, 32, 64, 384, 960, 1280, 960, 384, 64, 128, 896, 2688, 4480, 4480, 2688, 896, 128, 256, 2048, 7168, 14336, 17920, 14336, 7168, 2048, 256, 512, 4608, 18432, 43008 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Triangle obtained from expansion of (2+2x)^n.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

B. N. Cyvin et al., Isomer enumeration of unbranched catacondensed polygonal systems with pentagons and heptagons, Match, No. 34 (Oct 1996), pp. 109-121.

Franck Ramaharo, Statistics on some classes of knot shadows, arXiv:1802.07701 [math.CO], 2018.

Franck Ramaharo, A generating polynomial for the pretzel knot, arXiv:1805.10680 [math.CO], 2018.

FORMULA

E.g.f. for column k: 2^k*x^k/k!*exp(2*x). - Geoffrey Critzer, Feb 13 2014

EXAMPLE

1,

2,   2,

4,   8,    4,

8,   24,   24,   8,

16,  64,   96,   64,    16,

32,  160,  320,  320,   160,   32,

64,  384,  960,  1280,  960,   384,   64,

128, 896,  2688, 4480,  4480,  2688,  896, 128,

256, 2048, 7168, 14336, 17920, 14336, 7168, 2048, 256

MATHEMATICA

nn=8; Map[Select[#, #>0&]&, Transpose[Table[Range[0, nn]!CoefficientList[Series[2^k x^k/k! Exp[2x], {x, 0, nn}], x], {k, 0, nn}]]]//Grid (* Geoffrey Critzer, Feb 13 2014 *)

Flatten[Table[Binomial[i, j]2^i, {i, 0, 10}, {j, 0, i}]] (* Harvey P. Dale, May 28 2015 *)

PROG

(PARI) for(n=0, 10, for(k=0, n, print1(binomial(n, k)*2^n, ", "))) \\ ~~~

(MAGMA) [[Binomial(n, k)*2^n: k in [0..n]]: n in [0..10]]; // G. C. Greubel, Oct 17 2018

CROSSREFS

Row sums : A000302 (powers of 4).

Sequence in context: A317011 A316876 A317604 * A240484 A240636 A281344

Adjacent sequences:  A038205 A038206 A038207 * A038209 A038210 A038211

KEYWORD

nonn,tabl,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 20 17:04 EST 2020. Contains 332080 sequences. (Running on oeis4.)