This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A060690 #52 Jul 02 2025 16:02:01
%S A060690 1,2,10,120,3876,376992,119877472,131254487936,509850594887712,
%T A060690 7145544812472168960,364974894538906616240640,
%U A060690 68409601066028072105113098240,47312269462735023248040155132636160,121317088003402776955124829814219234385920
%N A060690 a(n) = binomial(2^n + n - 1, n).
%C A060690 Also the number of n X n (0,1) matrices modulo rows permutation (by symmetry this is the same as the number of (0,1) matrices modulo columns permutation), i.e., the number of equivalence classes where two matrices A and B are equivalent if one of them is the result of permuting the rows of the other. The total number of (0,1) matrices is in sequence A002416.
%C A060690 Row sums of A220886. - _Geoffrey Critzer_, Nov 20 2014
%H A060690 Harry J. Smith, <a href="/A060690/b060690.txt">Table of n, a(n) for n = 0..59</a>
%F A060690 a(n) = [x^n] 1/(1-x)^(2^n).
%F A060690 a(n) = (1/n!)*Sum_{k=0..n} ( (-1)^(n-k)*Stirling1(n, k)*2^(k*n) ). - _Vladeta Jovovic_, May 28 2004
%F A060690 a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(2^n+n,k) - _Vladeta Jovovic_, Jan 21 2008
%F A060690 a(n) = Sum_{k=0..n} Stirling1(n,k)*(2^n+n-1)^k/n!. - _Vladeta Jovovic_, Jan 21 2008
%F A060690 G.f.: A(x) = Sum_{n>=0} [ -log(1 - 2^n*x)]^n / n!. More generally, Sum_{n>=0} [ -log(1 - q^n*x)]^n/n! = Sum_{n>=0} C(q^n+n-1,n)*x^n ; also Sum_{n>=0} log(1 + q^n*x)^n/n! = Sum_{n>=0} C(q^n,n)*x^n. - _Paul D. Hanna_, Dec 29 2007
%F A060690 a(n) ~ 2^(n^2) / n!. - _Vaclav Kotesovec_, Jul 02 2016
%F A060690 a(n) = A163767(2^n). - _Alois P. Heinz_, Jun 12 2024
%p A060690 with(combinat): for n from 0 to 20 do printf(`%d,`,binomial(2^n+n-1, n)) od:
%t A060690 Table[Binomial[2^n+n-1,n],{n,0,20}] (* _Harvey P. Dale_, Apr 19 2012 *)
%o A060690 (PARI) a(n)=binomial(2^n+n-1,n)
%o A060690 (PARI) {a(n)=polcoeff(sum(k=0,n,(-log(1-2^k*x +x*O(x^n)))^k/k!),n)} \\ _Paul D. Hanna_, Dec 29 2007
%o A060690 (PARI) a(n) = sum(k=0, n, stirling(n,k,1)*(2^n+n-1)^k/n!); \\ _Paul D. Hanna_, Nov 20 2014
%o A060690 (Sage) [binomial(2^n +n-1, n) for n in (0..20)] # _G. C. Greubel_, Mar 14 2021
%o A060690 (Magma) [Binomial(2^n +n-1, n): n in [0..20]]; // _G. C. Greubel_, Mar 14 2021
%o A060690 (Python)
%o A060690 from math import comb
%o A060690 def A060690(n): return comb((1<<n)+n-1,n) # _Chai Wah Wu_, Jul 05 2024
%Y A060690 Sequences of the form binomial(2^n +p*n +q, n): A136556 (0,-1), A014070 (0,0), A136505 (0,1), A136506 (0,2), this sequence (1,-1), A132683 (1,0), A132684 (1,1), A132685 (2,0), A132686 (2,1), A132687 (3,-1), A132688 (3,0), A132689 (3,1).
%Y A060690 Cf. A002416, A060336, A088309, A163767.
%Y A060690 Cf. A136555, A220886.
%Y A060690 Main diagonal of A092056.
%Y A060690 Central terms of A137153.
%K A060690 nonn
%O A060690 0,2
%A A060690 Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 19 2001
%E A060690 More terms from _James Sellers_, Apr 20 2001
%E A060690 Edited by _N. J. A. Sloane_, Mar 17 2008