A171800 a(n) = ((n+1)*2^n + 1)*(2^n + 1)^(n-1).
1, 5, 65, 2673, 397953, 228882753, 520970490625, 4723480504289025, 170687922720157732865, 24563695027660686202250241, 14068441356460459384918212890625, 32058887942708146080692278858371608577, 290694663888102785007861162394348756446314497
Offset: 0
Examples
G.f.: A(x) = 1 + 5*x + 65*x^2 + 2673*x^3 + 397953*x^4 +... A(x) = 1/(1-x) + 2*2*x/(1-2*x)^2 + 3*2^4*x^2/(1-2^2*x)^3 + 4*2^9*x^3/(1-2^3*x)^4 +...
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..58
Programs
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Mathematica
Table[((n + 1)*2^n + 1)*(2^n + 1)^(n - 1), {n, 0, 15}] (* Wesley Ivan Hurt, Jan 19 2017 *) -
PARI
{a(n)=polcoeff(sum(m=0,n,(m+1)*2^(m^2)*x^m/(1-2^m*x+x*O(x^n))^(m+1)),n)} -
PARI
{a(n)=n!*polcoeff(sum(k=0, n, (k+1)*2^(k^2)*exp(2^k*x)*x^k/k!), n)} -
PARI
{a(n)=((n+1)*2^n+1)*(2^n+1)^(n-1)}
Formula
O.G.f.: Sum_{n>=0} (n+1)*2^(n^2) * x^n/(1 - 2^n*x)^(n+1).
E.g.f.: Sum_{n>=0} (n+1)*2^(n^2) * exp(2^n*x) * x^n/n!.