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A094262
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Triangle read by rows giving the coefficients of formulae generating each variety of S2(n,k) (Stirling numbers of 2nd kind). The p-th row (p>=1) contains T(i,p) for i=1 to 2*p-1, where T(i,p) satisfies Sum_{i=1..2*p-1} T(i,p) * C(n-p,i-1).
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11
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1, 1, 2, 1, 1, 6, 12, 10, 3, 1, 14, 61, 124, 131, 70, 15, 1, 30, 240, 890, 1830, 2226, 1600, 630, 105, 1, 62, 841, 5060, 16990, 35216, 47062, 40796, 22225, 6930, 945, 1, 126, 2772, 25410, 127953, 401436, 836976, 1196532, 1182195, 795718, 349020, 90090
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| The formulae S2(n+p-1,n) obtained are those of S2(n+1,n) { A000217 } (Triangular Numbers), S2(n+2,n) { A001296 }, S2(n+3,n) { A001297 }, S2(n+4,n) { A001298 } and so on.
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LINKS
| M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions (with Formulas, Graphs and Mathematical Tables), U.S. Dept. of Commerce, National Bureau of Standards, Applied Math. Series 55, 1964, 1046 pages (9th Printing: November 1970) - Combinatorial Analysis, Table 24.4, Stirling Numbers of the Second Kind (author: Francis L. Miksa), p. 835.
Eric Weisstein's World of Mathematics, Stirling numbers of the 2nd kind.
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EXAMPLE
| Row 5 contains 1,30,240,890,1830,2226,1600,630,105, so the formula generating S2(n+4,n) numbers
{ A001298 } will be the following : 1 +30*(n-5) +240*C(n-5,2) +890*C(n-5,3) +1830*C(n-5,4)
+2226*C(n-5,5) +1600*C(n-5,6) +630*C(n-5,7) +105*C(n-5,8). And then substituting for the 9th
number of such a S2(n+p-1,n) gives S2(13,9) = 359502.
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CROSSREFS
| Cf. A008277, A000217, A001296, A001297, A001298, A094216, A008275.
Sequence in context: A172107 A165891 A039763 * A123554 A105291 A025270
Adjacent sequences: A094259 A094260 A094261 * A094263 A094264 A094265
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Andre F. Labossiere (boronali(AT)laposte.net), Jun 01 2004
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