A129324 Third column of PE^2.

0, 0, 1, 6, 36, 220, 1410, 9534, 68040, 511704, 4046310, 33560010, 291244668, 2638581972, 24901833866, 244333004790, 2487900487440, 26245651191600, 286408960814862, 3228529392965250, 37544229610105220, 449858650676764140

Offset

0,4

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,3]; with exact integer arithmetic: PE=exp(matpascal(5)-matid(6)); A = PE^2; a(n)=A[n,3].

E.g.f.: (x^2/2) * exp(2 * (exp(x) - 1)). - Ilya Gutkovskiy, Jul 11 2020

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: A129324 := proc(n) A078937(n+1, 2) ; end: seq(A129324(n), n=0..23) ; # 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, 2];
a /@ Range[0, 21] (* Jean-François Alcover, Mar 24 2020, after R. J. Mathar *)

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: A033142 A082309 A004319 * A180218 A218991 A351056

Adjacent sequences: A129321 A129322 A129323 * A129325 A129326 A129327

Keyword

nonn,easy

Author

Gottfried Helms, Apr 08 2007

Extensions

More terms from R. J. Mathar, May 30 2008

Status

approved