The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A349479 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A349479

Irregular triangle read by rows: T(n,k) = S1(n,k)*2^k, where S1(n,k) is the associated Stirling number of the first kind (cf. A008306) (n >= 0, 0 <= k <= floor(n/2)).
(history; published version)

#24 by Andrew Howroyd at Tue Dec 28 14:13:17 EST 2021

STATUS

reviewed

approved

#23 by Michel Marcus at Tue Dec 28 13:36:07 EST 2021

STATUS

proposed

reviewed

#22 by Jean-François Alcover at Tue Dec 28 09:54:29 EST 2021

STATUS

editing

proposed

#21 by Jean-François Alcover at Tue Dec 28 09:53:53 EST 2021

MATHEMATICA

S1[0, 0] = 1; S1[_, 0] = 0; S1[n_, k_] /; k > Quotient[n, 2] = 0;

S1[n_, k_] := S1[n, k] = (n-1)*(S1[n-1, k] + S1[n-2, k-1]);

T[n_, k_] := S1[n, k]*2^k;

Table[T[n, k], {n, 0, 14}, {k, 0, Quotient[n, 2]}] // Flatten (* Jean-François Alcover, Dec 28 2021 *)

STATUS

approved

editing

#20 by Alois P. Heinz at Fri Dec 17 15:23:07 EST 2021

STATUS

editing

approved

#19 by Alois P. Heinz at Fri Dec 17 15:22:15 EST 2021

NAME

Irregular triangle read by rows: T(n,k) = S1(n,k)*2^k, where S1(n,k) is the associated Stirling number of the first kind (cf. A008306) (n >= 2, 1 0, 0 <= k <= floor(n/2)).

DATA

1, 0, 0, 2, 0, 4, 0, 12, 12, 0, 48, 80, 0, 240, 520, 120, 0, 1440, 3696, 1680, 0, 10080, 29232, 19040, 1680, 0, 80640, 256896, 211456, 40320, 0, 725760, 2493504, 2429280, 705600, 30240, 0, 7257600, 26547840, 29430720, 11285120, 1108800, 0, 79833600, 307992960, 378595008, 177580480, 27720000, 665280

OFFSET

2,1

0,4

EXAMPLE

[20] 21;

[31] 40;

[42] 12, 120, 2;

[53] 48, 800, 4;

[4] 0, 12, 12;

[5] 0, 48, 80;

[6] 0, 240, 520, 120;

[7] 0, 1440, 3696, 1680;

[8] 0, 10080, 29232, 19040, 1680;

[9] 0, 80640, 256896, 211456, 40320;

MAPLE

T:= n-> (p-> seq(coeff(p, x, i), i=10..degreefloor(pn/2)))(b(n)):

seq(T(n), n=20..14); # Alois P. Heinz, Nov 19 2021

STATUS

approved

editing

#18 by Michel Marcus at Fri Dec 10 23:13:44 EST 2021

STATUS

reviewed

approved

#17 by Andrew Howroyd at Fri Dec 10 23:01:00 EST 2021

STATUS

proposed

reviewed

#16 by Omar E. Pol at Thu Dec 09 05:23:03 EST 2021

STATUS

editing

proposed

#15 by Omar E. Pol at Thu Dec 09 05:22:49 EST 2021

EXAMPLE

[2] 2;

[3] 4;

[4] 12, 12;

[5] 48, 80;

[6] 240, 520, 120;

[7] 1440, 3696, 1680;

[8] 10080, 29232, 19040, 1680;

...

STATUS

approved

editing

Discussion

Thu Dec 09

05:23

Omar E. Pol: Minor edits.