A358606 -id:A358606 - cp's OEIS frontend

A358603 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * (n-k)!/(n-2*k)!.

1, 1, 0, -1, 0, 3, 2, -9, -12, 35, 78, -153, -544, 723, 4170, -3337, -35028, 10851, 320678, 57255, -3178152, -2190253, 33864546, 42120183, -385314460, -719159517, 4649508222, 12033407591, -59076411312, -204022615725, 784134861818, 3554417974647, -10768948801764

Offset: 0

Seiichi Manyama, Nov 23 2022

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Seiichi Manyama, Table of n, a(n) for n = 0..899

Cf. A358604, A358605, A358606.

Cf. A122852.

nxt[{n_,a_,b_}]:={n+1,b,(b-a(n+1)+1)/2}; NestList[nxt,{1,1,1},40][[;;,2]] (* Harvey P. Dale, Jul 25 2024 *)

a(n) = sum(k=0, n\2, (-1)^k*(n-k)!/(n-2*k)!);

a(n) = (a(n-1) - n * a(n-2) + 1)/2 for n > 1.

A358604 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * (n-2k)!/(n-3k)!.

Original entry on oeis.org

1, 1, 1, 0, -1, -2, -1, 2, 7, 8, -1, -26, -49, -28, 103, 314, 359, -344, -2113, -3682, -161, 14684, 36791, 25762, -100297, -373456, -472241, 587846, 3877487, 7149988, -1111801, -40808566, -103472249, -56751688, 424662623, 1490284654, 1674543359, -4121143444

Offset: 0

Seiichi Manyama, Nov 23 2022

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Seiichi Manyama, Table of n, a(n) for n = 0..1000

Cf. A358603, A358605, A358606.

Cf. A357532.

a(n) = sum(k=0, n\3, (-1)^k*(n-2*k)!/(n-3*k)!);

a(n) = (2 * a(n-1) - n * a(n-3) + 1)/3 for n > 2.

A358605 a(n) = Sum_{k=0..floor(n/4)} (-1)^k * (n-3k)!/(n-4k)!.

Original entry on oeis.org

1, 1, 1, 1, 0, -1, -2, -3, -2, 1, 6, 13, 16, 9, -14, -59, -108, -119, -26, 261, 736, 1177, 1026, -731, -4964, -11079, -14978, -6299, 30024, 102841, 189466, 190917, -97004, -921191, -2301354, -3396539, -1674368, 7265241, 27311794, 53600101, 56943756, -31760903, -310594514, -809146971

Offset: 0

Seiichi Manyama, Nov 23 2022

sign

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Cf. A358603, A358604, A358606.

Cf. A357533.

a(n) = sum(k=0, n\4, (-1)^k*(n-3*k)!/(n-4*k)!);

a(n) = (3 * a(n-1) - n * a(n-4) + 1)/4 for n > 3.

cp's OEIS Frontend

A358603 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * (n-k)!/(n-2*k)!.

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Formula

A358604 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * (n-2k)!/(n-3k)!.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

A358605 a(n) = Sum_{k=0..floor(n/4)} (-1)^k * (n-3k)!/(n-4k)!.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

cp's OEIS Frontend

A358603 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * (n-k)!/(n-2*k)!.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A358604 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * (n-2*k)!/(n-3*k)!.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

A358605 a(n) = Sum_{k=0..floor(n/4)} (-1)^k * (n-3*k)!/(n-4*k)!.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

A358604 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * (n-2k)!/(n-3k)!.

A358605 a(n) = Sum_{k=0..floor(n/4)} (-1)^k * (n-3k)!/(n-4k)!.