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Search: id:A093523
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| A093523 |
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Inverse binomial transform of A010054 (1 if triangular number else 0). |
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+0
2
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| 1, 0, -1, 3, -7, 14, -24, 34, -35, 8, 82, -298, 759, -1704, 3627, -7538, 15425, -30992, 60673, -114647, 206853, -351365, 549132, -752653, 784277, -162126, -2252600, 8950526, -25129652, 61349528, -138789534, 299803944, -629297799, 1298075184, -2650139349, 5375982063, -10849417306
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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The e.g.f., F(x) = exp(-x)*sum_{n>=0} x^(n*(n+1)/2)/(n*(n+1)/2)!, is approximated by 1/sqrt(2x) for x>1; example: F(1)=0.79758, F(2)=0.59852, F(10)=0.23183, F(50)=0.10063.
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FORMULA
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E.g.f.: exp(-x)*sum_{n>=0} x^(n*(n+1)/2)/(n*(n+1)/2)!
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PROGRAM
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(PARI) {a(n)=n!*polcoeff((sum(k=0, sqrtint(2*n+1), x^(k*(k+1)/2)/(k*(k+1)/2)!)*sum(j=0, n, (-x)^j/j!)+x*O(x^n)), n)}
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CROSSREFS
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Sequence in context: A115285 A004232 A140462 this_sequence A123386 A060999 A089187
Adjacent sequences: A093520 A093521 A093522 this_sequence A093524 A093525 A093526
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KEYWORD
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sign
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Mar 30 2004
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