login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A135742
E.g.f.: A(x) = Sum_{n>=0} exp( n*(n-1)/2 * x ) * x^n / n!.
6
1, 1, 1, 4, 19, 131, 1156, 12622, 166825, 2600677, 47038456, 974165336, 22829939089, 599668759483, 17512623094240, 564613124026876, 19972670155565761, 771019774737952313, 32326390781950804048
OFFSET
0,4
LINKS
FORMULA
a(n) = Sum_{k=0..n} C(n,k) * ( k*(k-1)/2 )^(n-k).
O.g.f.: Sum_{n>=0} x^n / (1 - n*(n-1)/2 * x)^(n+1). - Paul D. Hanna, Jul 30 2014
MATHEMATICA
Flatten[{1, Table[Sum[Binomial[n, k]*Binomial[k, 2]^(n - k), {k, 0, n}], {n, 1, 25}]}] (* G. C. Greubel, Nov 05 2016 *)
PROG
(PARI) {a(n)=sum(k=0, n, binomial(n, k)*(k*(k-1)/2)^(n-k))}
for(n=0, 25, print1(a(n), ", "))
(PARI) {a(n)=n!*polcoeff(sum(k=0, n, exp(k*(k-1)/2*x +x*O(x^n))*x^k/k!), n)}
for(n=0, 25, print1(a(n), ", "))
(PARI) /* From Sum_{n>=0} x^n/(1 - n*(n-1)/2*x)^(n+1): */
{a(n)=polcoeff(sum(k=0, n, x^k/(1-k*(k-1)/2*x +x*O(x^n))^(k+1)), n)}
for(n=0, 25, print1(a(n), ", "))
CROSSREFS
Cf. variants: A135743, A135744, A135745, A135746.
Sequence in context: A352327 A305867 A121681 * A144273 A127060 A134147
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 27 2007
STATUS
approved