A132945 Generalization of an a(n)=3*2^n*a(n-1) as 3=(m+1) and 2=m To give general term: t(n,m)=a(n)=(m+1)^n*m^(n*(n-1)/2).

1, 1, 2, 1, 4, 18, 1, 8, 216, 1728, 1, 16, 5184, 186624, 2560000, 1, 32, 248832, 60466176, 3276800000, 75937500000, 1, 64, 23887872, 58773123072, 16777216000000, 1423828125000000, 55316793250381824, 1, 128, 4586471424

Offset

1,3

Comments

From the ratio: a[2*n+1]/a[n]=(p/q)^(2*n)/(1/q)^(2*n+1)=q*p^(2*n) where p/q+1/q=1 or q=p+1 to give a[2*n+1]=(p+1)*p^(2*n)*a[2*n) Substitution of 2*n+1=m gives: a[m]=(p+1)*p^(m-1)*a[m] The general term is: a[n]=(p+1)^n*p(n*n-1)/2) Tha generalizes to the triangular sequence: t{n,m]=(m+1)^n*m^(n*(n-1)/2) There are a sequence of integer sequences. The row sums are: Table[Apply[Plus, Table[If[m == 0, 1, (m + 1)^n*m^(n*(n - 1)/2)], {m, 0, n}]], {n, 0, 10}]; {1, 3, 23, 1953, 2751825, 79275015041, 56757457388392833, 1189555425750705365861377, 840397436855599094944934404993537, 22654481007347397384838896692805197152547329, 26024856222487890805745042737267875522571222279183006721}

Links

Table of n, a(n) for n=1..31.

Formula

If m==0,t(n,0)=1 else t(n,m)=a(n)=(m+1)^n*m^(n*(n-1)/2)

Example

{1},
{1, 2},
{1, 4, 18},
{1, 8, 216, 1728},
{1, 16, 5184, 186624, 2560000},
{1, 32, 248832, 60466176, 3276800000, 75937500000},
{1, 64, 23887872, 58773123072, 16777216000000, 1423828125000000, 55316793250381824}

Mathematica

a = Table[Table[If[m == 0, 1, (m + 1)^n*m^(n*(n - 1)/2)], {m, 0, n}], {n, 0, 10}]; Flatten[a]

Crossrefs

Sequence in context: A238454 A025228 A267377 * A192494 A013156 A012925

Adjacent sequences: A132942 A132943 A132944 * A132946 A132947 A132948

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Nov 19 2007

Status

approved