0,2

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 (helms(AT)uni-kassel.de), 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 (pbarry(AT)wit.ie), Nov 26 2008]

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 (helms(AT)uni-kassel.de), 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.

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}, ...

(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 (helms(AT)uni-kassel.de), Apr 08 2007

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 this_sequence A167560 A132159 A112356

Adjacent sequences: A078934 A078935 A078936 this_sequence A078938 A078939 A078940

nonn,tabl

Paul D. Hanna (pauldhanna(AT)juno.com), Dec 18 2002

Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Apr 25 2007