A371686 - OEIS

A371686

Triangle read by rows: T(n, k) = e * binomial(n, k) * Gamma(k + 1, 1).

1, 1, 2, 1, 4, 5, 1, 6, 15, 16, 1, 8, 30, 64, 65, 1, 10, 50, 160, 325, 326, 1, 12, 75, 320, 975, 1956, 1957, 1, 14, 105, 560, 2275, 6846, 13699, 13700, 1, 16, 140, 896, 4550, 18256, 54796, 109600, 109601, 1, 18, 180, 1344, 8190, 41076, 164388, 493200, 986409, 986410

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..54.

FORMULA

T(n, k) = (n! / (n - k)!)*(Sum_{j = 0..k} (1 / j!)). - Detlef Meya, Apr 06 2024

EXAMPLE

Triangle starts:

[0] 1;

[1] 1, 2;

[2] 1, 4, 5;

[3] 1, 6, 15, 16;

[4] 1, 8, 30, 64, 65;

[5] 1, 10, 50, 160, 325, 326;

[6] 1, 12, 75, 320, 975, 1956, 1957;

[7] 1, 14, 105, 560, 2275, 6846, 13699, 13700;

MAPLE

T := (n, k) -> binomial(n, k)*GAMMA(k + 1, 1)*exp(1):

seq(seq(simplify(T(n, k)), k = 0..n), n = 0..9);

MATHEMATICA

T[n_, k_]:=(n!/(n-k)!)*Sum[1/j!, {j, 0, k}]; Flatten[Table[T[n, k], {n, 0, 9}, {k, 0, n}]] (* Detlef Meya, Apr 06 2024 *)

CROSSREFS

Cf. A000522 (main diagonal), A007526 (subdiagonal), A010842 (row sums), A000142 and A133942 (alternating row sums), A367963 (central terms).

Sequence in context: A124959 A081281 A108198 * A321000 A121289 A211561

Adjacent sequences: A371683 A371684 A371685 * A371687 A371688 A371689

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Apr 03 2024

STATUS

approved