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 A053567 Stirling numbers of first kind, s(n+5, n). 8
 -120, 1764, -13132, 67284, -269325, 902055, -2637558, 6926634, -16669653, 37312275, -78558480, 156952432, -299650806, 549789282, -973941900, 1672280820, -2792167686, 4546047198, -7234669596, 11276842500, -17247104875, 25922927745, -38343278610, 55880640270 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 833. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..200 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]. G. C. Greubel, A Note on Jain basis functions, arXiv:1612.09385 [math.CA], 2016. FORMULA a(n) = (-1)^n*binomial(n+5, 6)*binomial(n+5, 2)*(3*n^2 + 23*n + 38)/8. G.f.: x*(120 + 444*x + 328*x^2 + 52*x^3 + x^4)/(1-x)^11. See row k=4 of triangle A112007 for the coefficients. E.g.f. with offset 5: exp(x)*(Sum_{m=0..5} A112486(5, m)*(x^(5+m)/(5+m)!). a(n) = binomial(n+5, 6)*binomial(n+5, 2)*(3*n^2 + 23*n + 38)/8. From the g.f. a(n) = (f(n+4, 5)/10!)*Sum_{m=0..min(5, n-1)} A112486(5, m)*f(10, 5-m)*f(n-1, m)), with the falling factorials f(n, m):=n*(n-1)*, ..., *(n-(m-1)). From the e.g.f. MAPLE A053567 := proc(n) (-1)^(n+1)*combinat[stirling1](n+5, n) ; end proc: # R. J. Mathar, Jun 08 2011 MATHEMATICA Table[StirlingS1[n+5, n](-1)^(n-1), {n, 30}] (* Harvey P. Dale, Sep 21 2011 *) PROG (Sage) [stirling_number1(n, n-5)*(-1)^(n+1) for n in xrange(6, 26)] # Zerinvary Lajos, May 16 2009 (MAGMA) [(-1)^n*Binomial(n+5, 6)*Binomial(n+5, 2)*(3*n^2+23*n+38)/8: n in [1..30]]; // Vincenzo Librandi, Jun 09 2011 (PARI) a(n) = (-1)^(n-1)*stirling(n+5, n, 1); \\ Michel Marcus, Aug 29 2017 CROSSREFS Next |Stirling1| diagonal A112002, 5th diagonal of A130534. Sequence in context: A027795 A223427 A282899 * A056270 A001118 A052767 Adjacent sequences:  A053564 A053565 A053566 * A053568 A053569 A053570 KEYWORD easy,sign,changed AUTHOR Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 17 2000 EXTENSIONS Definition edited by Eric M. Schmidt, Aug 29 2017 STATUS approved

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Last modified May 22 13:47 EDT 2018. Contains 304425 sequences. (Running on oeis4.)