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 A051142 Generalized Stirling number triangle of first kind. 12
 1, -4, 1, 32, -12, 1, -384, 176, -24, 1, 6144, -3200, 560, -40, 1, -122880, 70144, -14400, 1360, -60, 1, 2949120, -1806336, 415744, -47040, 2800, -84, 1, -82575360, 53526528, -13447168, 1732864, -125440, 5152, -112, 1, 2642411520, -1795424256, 483835904 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n,m)= R_n^m(a=0,b=4) in the notation of the given reference. a(n,m) is a Jabotinsky matrix, i.e., the monic row polynomials E(n,x) := sum(a(n,m)*x^m,m=1..n) = product(x-4*j,j=0..n-1), n >= 1, E(0,x) := 1, are exponential convolution polynomials (see A039692 for the definition and a Knuth reference). This is the signed Stirling1 triangle with diagonal d>=0 (main diagonal d=0) scaled with 4^d. Also the Bell transform of the quadruple factorial numbers Product_{k=0..n-1} (4*k+4) (A047053) giving unsigned values and adding 1,0,0,0,... as column 0. For the definition of the Bell transform see A264428 and for cross-references A265606. - Peter Luschny, Dec 31 2015 REFERENCES Mitrinovic, D. S.; Mitrinovic, R. S.; Tableaux d'une classe de nombres relies aux nombres de Stirling. Univ. Beograd. Pubi. Elektrotehn. Fak. Ser. Mat. Fiz. No. 77 1962, 77 pp. LINKS Richell O. Celeste, Roberto B. Corcino, Ken Joffaniel M. Gonzales. Two Approaches to Normal Order Coefficients. Journal of Integer Sequences, Vol. 20 (2017), Article 17.3.5. W. Lang, First 10 rows. FORMULA a(n, m) = a(n-1, m-1) - 4*(n-1)*a(n-1, m), n >= m >= 1; a(n, m) := 0, n

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Last modified October 17 14:47 EDT 2019. Contains 328114 sequences. (Running on oeis4.)