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A040075
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5-fold convolution of A000302 (powers of 4); expansion of 1/(1-4*x)^5.
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14
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1, 20, 240, 2240, 17920, 129024, 860160, 5406720, 32440320, 187432960, 1049624576, 5725224960, 30534533120, 159719096320, 821412495360, 4161823309824, 20809116549120, 102821517066240, 502682972323840
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Also convolution of A020920 with A000984 (central binomial coefficients).
With a different offset, number of n-permutations (n=5) of 5 objects u, v, w, z, x with repetition allowed, containing exactly four (4)u's. Example: a(1)=20 because we have uuuuv, uuuvu, uuvuu, uvuuu, vuuuu, uuuuw, uuuwu, uuwuu, uwuuu, wuuuu, uuuuz, uuuzu, uuzuu, uzuuu, zuuuu, uuuux, uuuxu, uuxuu, uxuuu and xuuuu. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 19 2008
Also convolution of A000302 with A038846, also convolution of A002457 with A020918, also convolution of A002697 with A038845, also convolution of A002802 with A002802. [From Rui Duarte, Oct 08 2011]
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Vincenzo Librandi, Table of n, a(n) for n = 0..400
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FORMULA
| a(n)=binomial(n+4, 4)*4^n; G.f. 1/(1-4*x)^5.
a(n) = sum( i_1+i_2+i_3+i_4+i_5+i_6+i_7+i_8+i_9+i_10=n, f(i_1)*f(i_2)*f(i_3)*f(i_4)*f(i_5)*f(i_6)*f(i_7)*f(i_8)*f(i_9)*f(i_10)) with f(k)=A000984(k) [From Rui Duarte, Oct 08 2011]
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MAPLE
| seq(seq(binomial(i, j)*4^(i-4), j =i-4), i=4..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 03 2007
seq(binomial(n+4, 4)*4^n, n=0..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 19 2008
spec := [S, {B=Set(Z, 0 <= card), S=Prod(Z, Z, Z, Z, B, B, B, B)}, labeled]: seq(combstruct[count](spec, size=n)/24, n=4..22); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 05 2009]
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PROG
| (Other) SAGE: [lucas_number2(n, 4, 0)*binomial(n, 4)/2^8 for n in xrange(4, 26)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 11 2009]
(MAGMA) [4^n*Binomial(n+4, 4): n in [0..30]]; // Vincenzo Librandi, Oct 15 2011
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CROSSREFS
| Cf. A000302, A020920, A000984.
Cf. A038231.
Sequence in context: A061139 A061121 A073398 * A138442 A140124 A123954
Adjacent sequences: A040072 A040073 A040074 * A040076 A040077 A040078
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KEYWORD
| easy,nonn
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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