A394443 a(n) = Sum_{k=0..n} Sum_{j=0..k} (-1)^(k - j) * binomial(k, j) * j^n * 2^j.

1, 2, 14, 156, 2404, 47310, 1133362, 32005400, 1041071208, 38332962810, 1576117028870, 71578863309492, 3558526264337420, 192218569184875142, 11210020924481677690, 702004358782658232240, 46983434611147824097104, 3346765071252016227670386, 252810562072190606804106894

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..362

Formula

a(n) = Sum_{k=0..n} A394444(n, k).

Maple

a := n -> local j, k; add(add((-1)^(k-j)*binomial(k, j)*j^n*2^j, j = 0..k), k = 0..n): seq(a(n), n = 0..18);
# Alternative:
b:= proc(n, k) option remember;
     `if`(n=0, 1, k*(b(n-1, k)+b(n-1, k-1)))
    end:
a:= n-> add(b(n, k), k=0..n):
seq(a(n), n=0..18);  # Alois P. Heinz, Apr 28 2026

Crossrefs

Cf. A394444.

Sequence in context: A175564 A355114 A332693 * A196791 A349312 A218295

Adjacent sequences: A394440 A394441 A394442 * A394444 A394445 A394446

Keyword

nonn

Author

Peter Luschny, Mar 20 2026

Status

approved