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Search: id:A154286
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| A154286 |
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a(n) = E(k)C(n+k,k) = Euler(k)*Pascal(n+k,k) for k=4. |
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+0
2
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| 5, 25, 75, 175, 350, 630, 1050, 1650, 2475, 3575, 5005, 6825, 9100, 11900, 15300, 19380, 24225, 29925, 36575, 44275, 53130, 63250, 74750, 87750, 102375, 118755, 137025, 157325, 179800, 204600, 231880, 261800, 294525
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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+ a(n) = E(4)binom{n+4}{4} where E(n) are the Euler number in the enumeration A122045.
+ a(n) is the special case k=4 in the sequence of diagonals in the triangel A153641.
+ a(n) is the 5-th row in A093375.
+ a(n) is the 5-th column in A103406.
+ a(n) is the 5-th antidiagonal in A103283.
+ (a(n+1)-a(n))/5 are the pyramidal numbers A000292 (n>1).
+ (a(n+2)-2a(n+1)+a(n))/5 are the triangular numbers A000217 (n>2).
+ (a(n+3)-3a(n+2)+3a(n+1)-a(n))/5 are the natural numbers A000027 (n>3).
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FORMULA
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a(n) = n*(n+1)*(n+2)*(n+3)*5/24;
a(n) = a(n-1)*(n+4)/n (n>0), a(0)=5;
ogf: 5/(1-x)^5;
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MAPLE
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seq(euler(4)*binomial(n+4, 4), n=0..32);
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CROSSREFS
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A000217, A153641.
Sequence in context: A146665 A059302 A147130 this_sequence A078234 A056374 A062989
Adjacent sequences: A154283 A154284 A154285 this_sequence A154287 A154288 A154289
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KEYWORD
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easy,nonn
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AUTHOR
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Peter Luschny (peter(AT)luschny.de), Jan 06 2009
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