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A059115
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Expansion of ((1-x)/(1-2*x))*exp(x/(1-x)).
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3
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1, 2, 9, 58, 485, 4986, 60877, 861554, 13878153, 250854130, 5030058161, 110837000682, 2662669300909, 69270266115818, 1940260799150325, 58220372514830626, 1863293173842259217, 63356877145370671074
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| L'(n,i) are unsigned Lah numbers (Cf. A008297):L'(n,i)=n!/i!*binomial(n-1,i-1) for i >= 1, L'(0,0)=1, L'(n,0)=0 for n>0.
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FORMULA
| Sum_{m=0..n} Sum_{i=0..n} L'(n, i)*Product_{j=1..m} (i-j+1).
Given g.f. A(x), then g.f. A000522 = A(x/(1+x)). - Michael Somos Aug 03 2006
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EXAMPLE
| (1-x)/(1-2*x)*exp(x/(1-x))=1+2*x+9/2*x^2+29/3*x^3+485/24*x^4+831/20*x^5+...
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MAPLE
| s := series((1-x)/(1-2*x)*exp(x/(1-x)), x, 21): for i from 0 to 20 do printf(`%d, `, i!*coeff(s, x, i)) od:
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PROG
| (PARI) {a(n)=if(n<0, 0, n!*polcoeff( (1-x)/(1-2*x)*exp(x/(1-x)+x*O(x^n)), n))} /* Michael Somos Aug 03 2006 */
(PARI) {a(n)=local(A); if(n<0, 0, n++; A=vector(n); A[n]=1; for(k=1, n-1, A[n-k]=1; if(k>1, A[n-k+1]=A[n-k+2]); for(i=n-k+1, n, A[i]=A[i-1]+k*A[i])); A[n])} /* Michael Somos Aug 03 2006 */
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CROSSREFS
| Row sums of A059114, A059110, A049020, A001861, A059099, A052897.
Sequence in context: A168358 A132608 A080834 * A156129 A191811 A005364
Adjacent sequences: A059112 A059113 A059114 * A059116 A059117 A059118
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 06 2001
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