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A217487 Partial sums of the squares of the numbers in sequence A080253. 5
1, 10, 299, 21908, 2901717, 602319006, 180257075455, 73470070612264, 39124516839956393, 26373727254869321522, 21951183825927218885331, 22108623093930072226980540, 26501124576166085360405809789, 37282620382364481062065321327558 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = sum(c(k)^2,k=0..n), where c(n) = A080253(n).
a(n) ~ (n!)^2 * 2^(2*n-1) / (log(2))^(2*n + 2). - Vaclav Kotesovec, Nov 27 2017
MATHEMATICA
t[n_] := Sum[StirlingS2[n, k] k!, {k, 0, n}]; c[n_] := Sum[Binomial[n, k] 2^k t[k], {k, 0, n}]; Table[Sum[c[k]^2, {k, 0, n}], {n, 0, 100}]
PROG
(Maxima) t(n):=sum(stirling2(n, k)*k!, k, 0, n);
c(n):=sum(binomial(n, k)*2^k*t(k), k, 0, n);
makelist(sum(c(k)^2, k, 0, n), n, 0, 40);
CROSSREFS
Sequence in context: A059072 A000459 A125288 * A173479 A173478 A069672
KEYWORD
nonn
AUTHOR
Emanuele Munarini, Oct 04 2012
STATUS
approved

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Last modified March 28 14:02 EDT 2024. Contains 371254 sequences. (Running on oeis4.)