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Search: id:A076051
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| A076051 |
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Sum of product of odd numbers <= n and the product of even numbers <= n. |
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+0
1
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| 1, 3, 5, 11, 23, 63, 153, 489, 1329, 4785, 14235, 56475, 181215, 780255, 2672145, 12348945, 44781345, 220253985, 840523635, 4370620275, 17465201775, 95498916975, 397983749625, 2278224696825, 9867844134225, 58917607974225
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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a(n) = o(n)+ e(n) where; o(n)=the product of odd numbers from 1 to n e(n)=the product of even numbers from 2 to n
Formula: a(n) = A060696(n+1) = A037223(n) + abs(A055634(n)) = A037223(n) + n! / A037223(n), A037223(n)=2^floor(n/2)*floor(n/2)!, for n>=2. Recurrence: a(1)=1, a(2)=3, a(3)=5, a(n) = (n-1)a(n-2)+(n-2)!! for n >= 4. Exponential generating function: x+(1+x+x^2)*(exp(x^2/2)*(1+sqrt(Pi/2)*erf(x/sqrt(2)))), where erf denotes the error function. - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Nov 01 2002
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CROSSREFS
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Adjacent sequences: A076048 A076049 A076050 this_sequence A076052 A076053 A076054
Sequence in context: A074892 A074874 A051439 this_sequence A018116 A018008 A104545
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KEYWORD
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easy,nonn
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AUTHOR
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Emrehan Halici (emrehan(AT)halici.com.tr), Oct 30 2002
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EXTENSIONS
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More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Nov 01 2002
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