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A038231 Triangle whose (i,j)-th entry is binomial(i,j)*4^(i-j). 18
1, 4, 1, 16, 8, 1, 64, 48, 12, 1, 256, 256, 96, 16, 1, 1024, 1280, 640, 160, 20, 1, 4096, 6144, 3840, 1280, 240, 24, 1, 16384, 28672, 21504, 8960, 2240, 336, 28, 1, 65536, 131072, 114688, 57344, 17920, 3584, 448, 32, 1, 262144, 589824 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Triangle of coefficients in expansion of (4+x)^n. - N-E. Fahssi, Apr 13 2008

REFERENCES

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

Naiomi T. Cameron and Asamoah Nkwanta, On Some (Pseudo) Involutions in the Riordan Group, Journal of Integer Sequences, Vol. 8 (2005), Article 05.3.7.

LINKS

Indranil Ghosh, Rows 0..125 of triangle, flattened

FORMULA

G.f. for j-th column is (x^j)/(1-4*x)^(j+1).

Convolution triangle of A000302 (powers of 4).

Sum_{k, 0<=k<=n} T(n,k)*(-1)^k*A000108(k)= A001700(n). - Philippe Deléham, Nov 27 2009

See A038207 and A027465 and replace 2 and 3 in analogous formulas with 4. - Tom Copeland, Oct 26 2012

EXAMPLE

1

4, 1

16, 8, 1

64, 48, 12, 1

256, 256, 96, 16, 1

1024, 1280, 640, 160, 20, 1

4096, 6144, 3840, 1280, 240, 24, 1

16384, 28672, 21504, 8960, 2240, 336, 28, 1

65536, 131072, 114688, 57344, 17920, 3584, 448, 32, 1

MAPLE

for i from 0 to 8 do seq(binomial(i, j)*4^(i-j), j = 0 .. i) od; # Zerinvary Lajos, Dec 21 2007

CROSSREFS

Cf. A013611 (row-reversed).

Sequence in context: A067425 A188481 A138681 * A104855 A143496 A143697

Adjacent sequences:  A038228 A038229 A038230 * A038232 A038233 A038234

KEYWORD

nonn,tabl,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 19 03:37 EST 2018. Contains 299330 sequences. (Running on oeis4.)