|
|
A173218
|
|
G.f.: A(x) = Sum_{n>=0} (1 + x)^(n^2+n) / 2^(n+1).
|
|
3
|
|
|
1, 4, 50, 1040, 30300, 1135080, 51972668, 2812429632, 175606496520, 12426817517920, 982846762742416, 85916923493646752, 8225856593959648696, 856044724445883011520, 96213518828394481754400
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ 2^(2*n) * n^n / (2^(log(2)/8) * log(2)^(2*n+1) * exp(n)). - Vaclav Kotesovec, Oct 08 2019
|
|
MATHEMATICA
|
Table[Sum[StirlingS1[n, j] * Sum[Binomial[j, s] * HurwitzLerchPhi[1/2, -j - s, 0], {s, 0, j}], {j, 0, n}] / (2*n!), {n, 0, 20}] (* Vaclav Kotesovec, Oct 08 2019 *)
|
|
PROG
|
(PARI) {a(n)=local(A=sum(m=0, n^2+100, (1+x +O(x^(n+2)))^(m*(m+1))/2^(m+1))); round(polcoeff(A, n))}
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|