A382676 a(n) = Sum_{k=0..n} (k!)^2 * binomial(k+2,2) * Stirling2(n+1,k+1)^2.

1, 4, 52, 1372, 60316, 3964684, 363503932, 44280657292, 6913081723516, 1345238707327564, 319137578070718012, 90648956570718822412, 30369040605677566161916, 11848724306426305222109644, 5325560174867275152102351292, 2731649923185995549312271694732

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Formula

a(n) = (n!)^2 * [(x*y)^n] exp(x+y) / (exp(x) + exp(y) - exp(x+y))^3.

Prog

(PARI) a(n) = sum(k=0, n, k!^2*binomial(k+2, 2)*stirling(n+1, k+1, 2)^2);

Crossrefs

Main diagonal of A382673.

Cf. A048163, A092552, A382678.

Sequence in context: A280571 A343429 A395386 * A277353 A055974 A009671

Adjacent sequences: A382673 A382674 A382675 * A382677 A382678 A382679

Keyword

nonn

Author

Seiichi Manyama, Apr 03 2025

Status

approved