A129325 Fourth column of PE^2.

0, 0, 0, 1, 8, 60, 440, 3290, 25424, 204120, 1705680, 14836470, 134240040, 1262060228, 12313382536, 124509169330, 1303109358880, 14098102762160, 157473907149600, 1813923418494126, 21523529286435000, 262809607270736540

Offset

0,5

Comments

Base matrix is in A011971; second power is in A078937; third power is in A078938; fourth power is in A078939.

Links

Table of n, a(n) for n=0..21.

Formula

PE=exp(matpascal(5))/exp(1); A = PE^2; a(n)=A[n,4] with exact integer arithmetic: PE=exp(matpascal(5)-matid(6)); A = PE^2; a(n)=A[n,4]

Maple

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: A129325 := proc(n) A078937(n+1, 3) ; end: seq(A129325(n), n=0..27) ; # R. J. Mathar, May 30 2008

Mathematica

A056857[n_, c_] := If[n <= c, 0, BellB[n - 1 - c] Binomial[n - 1, c]];
A078937[n_, c_] := Sum[A056857[n, k] A056857[k + 1, c], {k, 0, n}];
a[n_] := A078937[n + 1, 3];
a /@ Range[0, 21] (* Jean-François Alcover, Mar 24 2020, after R. J. Mathar *)

Prog

(PARI) m=matpascal(30)-matid(31); pe=matid(31)+sum(i=1, 30, m^i/i!); A=pe^2; A[, 4] \\ Herman Jamke (hermanjamke(AT)fastmail.fm), May 01 2008

Crossrefs

Cf. A056857, A078937, A078938, A078944, A078945, A000110.

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

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

Sequence in context: A126640 A093132 A094169 * A285391 A001267 A099156

Adjacent sequences: A129322 A129323 A129324 * A129326 A129327 A129328

Keyword

nonn,easy

Author

Gottfried Helms, Apr 08 2007

Extensions

More terms from R. J. Mathar and Herman Jamke (hermanjamke(AT)fastmail.fm), May 01 2008

Status

approved