0,2

Also, ways of placing n labeled balls into n unlabeled (but 4-colored) boxes. Binomial transform of this sequence is A078945 and a(n+1) = 4*A078945(n). - Paul D. Hanna (pauldhanna(AT)juno.com), Dec 08 2003

First column of PE^4, where PE is given in A011971, second power in A078937, third power in A078938, fourth power in A078939 - Gottfried Helms (helms(AT)uni-kassel.de), Apr 08 2007

PE=exp(matpascal(5))/exp(1); A = PE^4; a(n)= A[ n,1 ] with exact integer arithmetic: PE=exp(matpascal(5)-matid(6)); A = PE^4; a(n)=A[ n,1] - Gottfried Helms (helms(AT)uni-kassel.de), Apr 08 2007

E.g.f.: exp{4(e^x-1)}.

a(n) = exp(-4)*sum(k>=0, 4^k*k^n/k! ) - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 25 2003

G.f.: 4*(x/(1-x))*A(x/(1-x)) = A(x) - 1; four times the binomial transform equals this sequence shifted one place left. - Paul D. Hanna (pauldhanna(AT)juno.com), Dec 08 2003

a(n) = Sum_{k = 0..n} 4^k*A048993(n, k); A048993 : Stirling-2 numbers . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), May 09 2004

A056857 := proc(n, c) combinat[bell](n-1-c)*binomial(n-1, c) ; end: A078937 := proc(n, c) add( A056857(n, k)*A056857(k+1, c), k=0..n) ; end: A078938 := proc(n, c) add( A078937(n, k)*A056857(k+1, c), k=0..n) ; end: A078939 := proc(n, c) add( A078938(n, k)*A056857(k+1, c), k=0..n) ; end: A078944 := proc(n) A078939(n+1, 0) ; end: seq(A078944(n), n=0..25) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 30 2008

Table[n!, {n, 0, 20}]CoefficientList[Series[E^(4E^x-4), {x, 0, 20}], x]

sage: from sage.combinat.expnums import expnums2 sage: expnums(20, 4) - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 26 2008

Cf. A078939, A001861, A056857, A078944, A078945, A000110.

Cf. A078937, A078938, A129323, A129324, A129325, A027710.

Cf. A129327, A129328, A129329, A078944, A129331, A129332, A129333.

Sequence in context: A100328 A082298 A129378 this_sequence A158900 A127088 A128236

Adjacent sequences: A078941 A078942 A078943 this_sequence A078945 A078946 A078947

nonn

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

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 30 2008

Edited by N. J. A. Sloane (njas(AT)research.att.com), Jul 02 2008 at the suggestion of R. J. Mathar