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 A078937 Square of lower triangular matrix of A056857 (successive equalities in set partitions of n). 16
 1, 2, 1, 6, 4, 1, 22, 18, 6, 1, 94, 88, 36, 8, 1, 454, 470, 220, 60, 10, 1, 2430, 2724, 1410, 440, 90, 12, 1, 14214, 17010, 9534, 3290, 770, 126, 14, 1, 89918, 113712, 68050, 25424, 6580, 1232, 168, 16, 1, 610182, 809262, 511704, 204120, 57204, 11844, 1848 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS First column gives A001861 (values of Bell polynomials); row sums gives A035009 (STIRLING transform of powers of 2); Square of the matrix exp(P)/exp(1) given in A011971. - Gottfried Helms, Apr 08 2007. Base matrix in A011971 and in A056857, second power in this entry, third power in A078938, fourth power in A078939 Riordan array [exp(2*exp(x)-2),x], whose production matrix has e.g.f. exp(x*t)(t+2*exp(x)). [From Paul Barry, Nov 26 2008] LINKS FORMULA PE=exp(matpascal(5))/exp(1); A = PE^2; a(n)=A[n,column] with exact integer arithmetic: PE=exp(matpascal(5)-matid(6)); A = PE^2; a(n)=A[n,1] - Gottfried Helms, Apr 08 2007 Exponential function of 2*Pascal's triangle (taken as a lower triangular matrix) divided by e^2: [A078937] = (1/e^2)*exp(2*[A007318]) = [A056857]^2. EXAMPLE Rows: {1}, {2,1}, {6,4,1}, {22,18,6,1}, {94,88,36,8,1}, {454,470,220,60,10,1}, {2430,2724,1410,440,90,12,1}, {14214,17010,9534,3290,770,126,14,1}, ... PROG (PARI) m=matpascal(5)-matid(6); pe=matid(6)+m/1! + m^2/2!+m^3/3!+m^4/4!+m^5/5! ; A=pe^2; a(n) = A[n (sequentially read)] - Gottfried Helms, Apr 08 2007 CROSSREFS Cf. A056857, A001861, A035009. Cf. A078938, A078944, A078945, A000110. Cf. A078937, A078938, A129323, A129324, A129325, A027710. Cf. A129327, A129328, A129329, A078944, A129331, A129332, A129333. Sequence in context: A117852 A080245 A080247 * A167560 A132159 A112356 Adjacent sequences:  A078934 A078935 A078936 * A078938 A078939 A078940 KEYWORD nonn,tabl AUTHOR Paul D. Hanna, Dec 18 2002 EXTENSIONS Entry revised by N. J. A. Sloane, Apr 25 2007 STATUS approved

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Last modified September 20 18:52 EDT 2019. Contains 327245 sequences. (Running on oeis4.)