id:A162298 - OEIS Search Results

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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; listen)

	OFFSET	`1,19`
	COMMENT	`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.`
	EXAMPLE	k=2: 1^1+2^1+3^1+..+m^1=1m^1/2+1m^2/2; k=3: 1^2+2^2+3^2+..+m^2=1m^1/6+1m^2/2+1m^3/3; k=4: 1^3+2^3+3^3+..+m^3=0m^1/1+1m^2/4+1m^3/2+1m^4/4; k=5: 1^4+2^4+3^4+..+m^4=-1m^1/30+0m^2/1+1m^3/3+1m^4/2+1m^5/5; k=6: 1^5+2^5+3^5+..+m^5=0m^1/1-1m^2/12+0m^3/1+5m^4/12+1m^5/2+1m^6/6; k=7: 1^6+2^6+3^6+..+m^6=1m^1/42+0m^2/1-7m^3/42+0m^4/1+1m^5/2+1m^6/2+1m^7/7; k=8: 1^7+2^7+3^7+..+m^7=0m^1/1+1m^2/12+0m^3/1-7m^4/24+0m^5/1+7m^6/12+1m^7/2+1m^8/8; k=9: 1^8+2^8+3^8+..+m^8=-1m^1/30+0m^2/1+2m^3/9+0m^4/1-21m^5/45+0m^6/1+2m^7/3+1m^8/2+1m^9/9; k=10: 1^9+2^9+3^9+..+m^9=0m^1/1-3m^2/20+0m^3/1+1m^4/2+0m^5/1-7m^6/10+0m^7/1+15m^8/20+1m^9/2+1m^10/10;..
	CROSSREFS	`Cf. A000027, A000367, A162299.` `Sequence in context: A112991 A137373 A086464 this_sequence A146306 A119788 A059592` `Adjacent sequences: A162295 A162296 A162297 this_sequence A162299 A162300 A162301`
	KEYWORD	`uned,sign`
	AUTHOR	`Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jun 30 2009`
	EXTENSIONS	`Corrected by Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jul 02 2009`

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Last modified November 27 22:38 EST 2009. Contains 167602 sequences.

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