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A089902
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Antidiagonal sums of array A089900.
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2
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1, 3, 10, 40, 193, 1107, 7412, 56960, 495055, 4805327, 51540462, 605360184, 7726837413, 106484488843, 1575591323104, 24910186990320, 419042540060243, 7472730215908551, 140804433625595626, 2795108750920323336
(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 the 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_{k=0..n} sum_{i=0..k} (n-k)^(k-i)*binomial(k, i)*(i+1)!
O.g.f.: Sum_{m>=0, n>=1} n!*x^(m+n-1)/(1-m*x)^n - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 18 2003
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PROG
| (PARI) a(n)=if(n<0, 0, sum(k=0, n, sum(i=0, k, (n-k)^(k-i)*binomial(k, i)*(i+1)!)))
(PARI) a(n)=sum(k=0, n, sum(i=0, k, (n-k)^(k-i)*binomial(k, i)*(i+1)!)); (PARI) a(n)=polcoeff(sum(m=0, 2*n, sum(k=1, 2*n, k!*x^(m+k-1)/(1-m*x)^k), x*O(x^n)), n);
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CROSSREFS
| Cf. A089900, A089901, A000312.
Sequence in context: A151077 A003703 A136128 * A093133 A030817 A030845
Adjacent sequences: A089899 A089900 A089901 * A089903 A089904 A089905
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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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