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A038231
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Triangle whose (i,j)-th entry is binomial(i,j)*4^(i-j).
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16
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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; internal format)
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OFFSET
| 0,2
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COMMENTS
| T(i,j) is the number of i-permutations of 5 objects a,b,c,d,e, with repetition allowed, containing j a's. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 21 2007
Triangle of coefficients in expansion of (4+x)^n - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Apr 13 2008
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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.
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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). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 27 2009]
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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
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MAPLE
| for i from 0 to 8 do seq(binomial(i, j)*4^(i-j), j = 0 .. i) od; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 21 2007
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CROSSREFS
| Sequence in context: A067425 A188481 A138681 * A104855 A143496 A143697
Adjacent sequences: A038228 A038229 A038230 * A038232 A038233 A038234
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KEYWORD
| nonn,tabl,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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