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A162298
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Numerators of coefficients for sum of (k-1)th powers of m first numbers in formulae: Sum_{x=1..m} x^(k-1)=Sum_{y=1..k} a(k^2+y-1-2-3-..-k)*m^y/A162299(k^2+y-1-2-3-..-k) where k>1, a(1)=0 and A162299(1)=1.
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0, 1, 1, 1, 1, 1, 0, 1, 1, 1, -1, 0, 1, 1, 1, 0, -1, 0, 5, 1, 1, 1, 0, -7, 0, 1, 1, 1, 0, 1, 0, -7, 0, 7, 1, 1, -1, 0, 2, 0, -21, 0, 2, 1, 1, 0, -3, 0, 1, 0, -7, 0, 15, 1, 1, 5, 0, -1, 0, 1, 0, -1, 0, 5, 1, 1, 0, 5, 0, -33, 0, 11, 0, -11, 0, 11, 1, 1, -691, 0, 455, 0, -1001, 0, 858, 0, -1001, 0, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,19
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COMMENTS
| where a(1)/A162299(1)=1th Bernoulli number and a(k^2-2-3-..-k)/A162299(k^2-2-3-..-k)=(k+1)-th Bernoulli number.
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EXAMPLE
| k=2: 1^1+2^1+3^1+..+m^1=1*m^1/2+1*m^2/2; k=3: 1^2+2^2+3^2+..+m^2=1*m^1/6+1*m^2/2+1*m^3/3; k=4: 1^3+2^3+3^3+..+m^3=0*m^1/1+1*m^2/4+1*m^3/2+1*m^4/4; k=5: 1^4+2^4+3^4+..+m^4=-1*m^1/30+0*m^2/1+1*m^3/3+1*m^4/2+1*m^5/5; k=6: 1^5+2^5+3^5+..+m^5=0*m^1/1-1*m^2/12+0*m^3/1+5*m^4/12+1*m^5/2+1*m^6/6; k=7: 1^6+2^6+3^6+..+m^6=1*m^1/42+0*m^2/1-7*m^3/42+0*m^4/1+1*m^5/2+1*m^6/2+1*m^7/7; k=8: 1^7+2^7+3^7+..+m^7=0*m^1/1+1*m^2/12+0*m^3/1-7*m^4/24+0*m^5/1+7*m^6/12+1*m^7/2+1*m^8/8; k=9: 1^8+2^8+3^8+..+m^8=-1*m^1/30+0*m^2/1+2*m^3/9+0*m^4/1-21*m^5/45+0*m^6/1+2*m^7/3+1*m^8/2+1*m^9/9; k=10: 1^9+2^9+3^9+..+m^9=0*m^1/1-3*m^2/20+0*m^3/1+1*m^4/2+0*m^5/1-7*m^6/10+0*m^7/1+15*m^8/20+1*m^9/2+1*m^10/10;..
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CROSSREFS
| Cf. A000027, A000367, A162299.
Sequence in context: A196840 A196755 A199510 * A146306 A119788 A059592
Adjacent sequences: A162295 A162296 A162297 * A162299 A162300 A162301
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KEYWORD
| uned,sign
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AUTHOR
| Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jun 30 2009
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EXTENSIONS
| Corrected by Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jul 02 2009
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