A355004 a(n) = Sum_{k=0..n} A271703(k + n, n), row sums of A355005.

1, 3, 43, 1333, 63321, 4034341, 321994723, 30869387193, 3454384526353, 441903886812721, 63608031487665171, 10174227287873082853, 1790258521269694523113, 343669522619597368671933, 71473405251333054552561091, 16008271911444915765782477041, 3841639137772270982094393928353

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = A187535(n) * hypergeom([1, -n], [1 - 2*n, -2*n], -1].

From Vaclav Kotesovec, Jun 15 2022: (Start)

Recurrence: (n-1)^2 * n * (64*n^4 - 464*n^3 + 1244*n^2 - 1475*n + 663)*a(n) = (n-1)*(2*n-3)*(512*n^6 - 3968*n^5 + 11872*n^4 - 17336*n^3 + 12880*n^2 - 4597*n + 617)*a(n-1) + (2048*n^7 - 19968*n^6 + 78912*n^5 - 163216*n^4 + 191140*n^3 - 128857*n^2 + 48842*n - 8937)*a(n-2) + 4*(2*n-5)*(2*n-3)*(64*n^4 - 208*n^3 + 236*n^2 - 123*n + 32)*a(n-3).

a(n) ~ 2^(4*n - 1/2) * n^(n - 1/2) / (sqrt(Pi) * exp(n)). (End)

Maple

L := (n, k) -> ifelse(n = k, 1, binomial(n-1, k-1)*n! / k!):
seq(add(L(n + k, n), k = 0..n), n = 0..16);

Mathematica

Table[Sum[Binomial[n + k, n]*FactorialPower[n + k - 1, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jun 15 2022 *)

Crossrefs

Cf. A271703 (unsigned Lah), A355005, A187535.

Sequence in context: A201784 A364498 A340822 * A303159 A274387 A300988

Adjacent sequences: A355001 A355002 A355003 * A355005 A355006 A355007

Keyword

nonn

Author

Peter Luschny, Jun 15 2022

Status

approved