A358604 -id:A358604 - 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.

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

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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.

A358606 a(n) = Sum_{k=0..floor(n/5)} (-1)^k * (n-4k)!/(n-5k)!.

Original entry on oeis.org

1, 1, 1, 1, 1, 0, -1, -2, -3, -4, -3, 0, 5, 12, 21, 26, 21, 0, -43, -114, -195, -244, -195, 42, 581, 1440, 2421, 2990, 2157, -1644, -9955, -22974, -37515, -44248, -24219, 50310, 205661, 442140, 689997, 740906, 190245, -1534224, -4941355, -9887058, -14429619, -13255900, 3510141

Offset: 0

Seiichi Manyama, Nov 23 2022

sign

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

Cf. A358603, A358604, A358605.

Cf. A357570.

a(n) = sum(k=0, n\5, (-1)^k*(n-4*k)!/(n-5*k)!);

a(n) = (4 * a(n-1) - n * a(n-5) + 1)/5 for n > 4.

cp's OEIS Frontend

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

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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

A358606 a(n) = Sum_{k=0..floor(n/5)} (-1)^k * (n-4k)!/(n-5k)!.

Views

Author

Keywords

Links

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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

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

A358606 a(n) = Sum_{k=0..floor(n/5)} (-1)^k * (n-4*k)!/(n-5*k)!.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

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

A358606 a(n) = Sum_{k=0..floor(n/5)} (-1)^k * (n-4k)!/(n-5k)!.