A173219 G.f.: A(x) = Sum_{n>=0} (1 + x)^(n(n+1)/2) / 2^(n+1).

1, 2, 12, 124, 1800, 33648, 769336, 20796960, 648841680, 22945907520, 907036108432, 39631833652320, 1896696894062880, 98669609894805600, 5543804125505195040, 334563594743197602272, 21583554094995765302592

Offset: 0

Author

Paul D. Hanna, Mar 05 2010

Keywords

• nonn

Comments

a(n) is the number of nonnegative integer matrices with n distinct columns and any number of nonzero rows with 2 ones in every column and columns in decreasing lexicographic order. - Andrew Howroyd, Jan 15 2020

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..100

Crossrefs

Row n=2 of A331278.

Cf. A121251, A173217, A173218.

Programs

Mathematica

Table[Sum[StirlingS1[n, j] * Sum[Binomial[j, s]*HurwitzLerchPhi[1/2, -j - s, 0], {s, 0, j}] / 2^(j+1), {j, 0, n}] / n!, {n, 0, 20}] (* Vaclav Kotesovec, Oct 08 2019 *)

PARI

{a(n)=local(A=sum(m=0,n^2+100,(1+x +O(x^(n+2)))^(m*(m+1)/2)/2^(m+1)));round(polcoeff(A,n))}

Formula

a(n) = A265937(n)/2. - Vaclav Kotesovec, Oct 08 2019

a(n) ~ 2^n * n^n / (2^(log(2)/4) * log(2)^(2*n+1) * exp(n)). - Vaclav Kotesovec, Oct 08 2019

a(n) = 2*A121251(n) for n > 0. - Andrew Howroyd, Jan 15 2020