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A023881
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Number of partitions in expanding space: sigma(n,q) is the sum of the q-th powers of the divisors of n.
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8
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1, 1, 3, 12, 82, 725, 8811, 128340, 2257687, 45658174, 1052672116, 27108596725, 772945749970, 24137251258926, 819742344728692, 30069017799172228, 1184889562926838573, 49914141857616862435
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| G.f.: exp( Sum_{k>0} sigma_k(k) * x^k / k). - Michael Somos, Feb 15 2006
G.f.: Product_{n>=1} (1 - n^n*x^n)^(-1/n). - Paul D. Hanna, Mar 08 2011
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EXAMPLE
| 1 + x + 3*x^2 + 12*x^3 + 82*x^4 + 725*x^5 + 8811*x^6 + 128340*x^7 + 2257687*x^8 + ...
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PROG
| (PARI) {a(n) = if( n<0, 0, polcoeff( exp( sum( k=1, n, sigma(k, k) * x^k / k, x * O(x^n))), n))} /* Michael Somos, Feb 15 2006 */
(PARI) {a(n)=if(n<0, 0, polcoeff(prod(k=1, n, (1-k^k*x^k+x*O(x^n))^(-1/k)), n))} /* Paul D. Hanna */
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CROSSREFS
| Cf. A023882, A158952.
Sequence in context: A084565 A197445 A188227 * A067111 A171186 A051549
Adjacent sequences: A023878 A023879 A023880 * A023882 A023883 A023884
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KEYWORD
| nonn,changed
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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