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A089901
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Main diagonal of A089900, also the inverse hyperbinomial of A000312 (offset 1).
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2
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1, 3, 18, 159, 1848, 26595, 456048, 9073911, 205437312, 5214027267, 146602156800, 4522866752943, 151895344131072, 5516066815430691, 215373243256915968, 8996883483108522375, 400372897193449586688, 18908951043963993686019
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The n-th row of array A089900 is the n-th binomial transform of the factorials found in row 0: {1!,2!,3!,..,(n+1)!,..}. The hyperbinomial transform of this main diagonal gives: {1,4,27,..,(n+1)^(n+1),..}, which is the next lower diagonal in array A089900.
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FORMULA
| a(n) = sum_{i=0..n} n^(n-i)*C(n, i)*(i+1)!, a(n) = sum_{i=0..n} -(n-i-1)^(n-i-1)*C(n, i)*(i+1)^(i+1).
E.g.f.: 1/(1+LambertW(-x))^3. E.g.f.: (Sum (n+1)^(n+1)/n!*x^n)*(Sum -(n-1)^(n-1)/n!*x^n).
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PROG
| (PARI) /* As (n+1)-th term of the n-th binomial transform of {(n+1)!}: */ a(n)=if(n<0, 0, sum(i=0, n, n^(n-i)*binomial(n, i)*(i+1)!)); /* As (n+1)-th term of inverse hyperbinomial of {(n+1)^(n+1)}: */ a(n)=if(n<0, 0, sum(i=0, n, -(n-i-1)^(n-i-1)*binomial(n, i)*(i+1)^(i+1)));
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CROSSREFS
| Cf. A089900, A089902, A000312.
Sequence in context: A116956 A166887 A075678 * A067302 A052182 A115415
Adjacent sequences: A089898 A089899 A089900 * A089902 A089903 A089904
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Nov 14 2003
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