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A060946
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Trace of Vandermonde matrix of numbers 1,2,..n, i.e. the matrix A with A[i,j] = i^j, 1 <= i <= n, 0 <= j <= n-1.
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3
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1, 3, 12, 76, 701, 8477, 126126, 2223278, 45269999, 1045269999, 26982694600, 769991065288, 24068076187769, 817782849441913, 30010708874832538
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A member of the family of sequences defined by a(n) = sum_{i=1..n}[i*c(1)*..*c(r)]^(i-1); c(i) integers. Here c(1)=1. - Ctibor O. ZIZKA (ctibor.zizka(AT)seznam.cz), Feb 23 2008
Partial sum of A000169. The subsequence of prime values begins 3, 701, 45269999, no more through a(50). [From Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 12 2010]
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,100
C. P. Simoes, Teste de Desempenho Mental.
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FORMULA
| a(n) = sum k=1, ..n k^(k-1)
a(n) = SUM[i=1..n] A000169(i). [From Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 12 2010]
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EXAMPLE
| a(3) = 12 because the matrix is: 1,1,1 1,2,4 1,3,9 and the trace is 1+2+9 = 12
1 = 1^0; 3 = 1^0 + 2^1; 12 = 1^0 + 2^1 + 3^2; 76 = 1^0 + 2^1 + 3^2 + 4^3
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MAPLE
| a:=n->sum ((j+1)^j, j=0..n): seq(a(n), n=0..17); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 17 2008]
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MATHEMATICA
| Table[Sum[i^(i-1), {i, n}], {n, 15}]
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PROG
| (PARI) { for (n=1, 100, write("b060946.txt", n, " ", sum(k=1, n, k^(k - 1))); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 15 2009]
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CROSSREFS
| A000178, A001923.
Cf. A000169.
Cf. A000169. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 12 2010]
Sequence in context: A120591 A032114 A193162 * A121421 A108043 A058561
Adjacent sequences: A060943 A060944 A060945 * A060947 A060948 A060949
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KEYWORD
| nonn
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AUTHOR
| Ahmed Fares (ahmedfares(AT)my-deja.com), May 08 2001
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EXTENSIONS
| More terms from Zak Seidov (zakseidov(AT)yahoo.com), Jul 07 2003
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