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A112494
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Sixth diagonal of the Stirling2 triangle A048993 and sixth column of triangle A008278.
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0
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1, 63, 966, 7770, 42525, 179487, 627396, 1899612, 5135130, 12662650, 28936908, 62022324, 125854638, 243577530, 452329200, 809944464, 1404142047, 2364885369, 3880739170, 6220194750, 9759104355, 15015551265, 22693687380, 33738295500
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| a(n)= Stirling2(n+6, n) with Stirling2(n, m)=A048993(n, m). a(n)= A008278(n+5, 6).
a(n)= sum(A008517(5, m+1)*binomial(n+5-m, 2*5), m=0..4) from the o.g.f. See p. 257 eq. (6.43) of the R . L. Graham et al. book quoted in A008517.
A001298 (fifth diagonal, resp. column).
O.g.f. x*sum(A008517(5, m+1)*x^m, m=0..4)/(1-x)^11 with the fifth row [1, 52, 328, 444, 120] of the second-order Eulerian triangle A008517.
E.g.f. with offset n=-4: exp(x)*sum(A112493(5, m)*(x^(m+5))/(m+5)!, m=0..5) with the k=5 row [1, 57, 546, 1750, 2205, 945] of triangle A112493.
a(n)= sum(A112493(5, m)*binomial(n+4, 5+m), m=0..5) from the e.g.f. (coefficients from A112493(5, m) are [1, 57, 546, 1750, 2205, 945]).
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MATHEMATICA
| lst={}; Do[f=StirlingS2[n, n-5]; AppendTo[lst, f], {n, 5, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 27 2008]
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PROG
| (Other) sage: [stirling_number2(n, n-5) for n in xrange(6, 30)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 16 2009]
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CROSSREFS
| Sequence in context: A024004 A201886 A091027 * A183076 A132465 A202983
Adjacent sequences: A112491 A112492 A112493 * A112495 A112496 A112497
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 14 2005
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