A271466 -id:A271466 - cp's OEIS frontend

A271748 Number of set partitions of [n] such that 9 is the largest element of the last block.

8280, 29874, 117488, 495408, 2215148, 10419024, 51235748, 262138728, 1389893708, 7611839904, 42937377908, 248865777048, 1478955826268, 8994703967184, 55889046456068, 354251342263368, 2287372272350828, 15026157296580864, 100307242528430228, 679694909468957688

Offset: 9

Alois P. Heinz, Apr 13 2016

Alois P. Heinz, Table of n, a(n) for n = 9..1000
Wikipedia, Partition of a set
Index entries for linear recurrences with constant coefficients, signature (36,-546,4536,-22449,67284,-118124,109584,-40320).

Column k=9 of A271466.

Vec(2*x^9*(4140 - 134103*x + 1781452*x^2 - 12490518*x^3 + 49449082*x^4 - 109114599*x^5 + 121981810*x^6 - 51819984*x^7 + 20160*x^8) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*x)*(1 - 8*x)) + O(x^40)) \\ Colin Barker, Jan 05 2018

G.f.: 2*x^9 *(20160*x^8 -51819984*x^7 +121981810*x^6 -109114599*x^5 +49449082*x^4 -12490518*x^3 +1781452*x^2 -134103*x +4140) / Product_{j=1..8} (j*x-1).

a(n) = 36*a(n-1) - 546*a(n-2) + 4536*a(n-3) - 22449*a(n-4) + 67284*a(n-5) - 118124*a(n-6) + 109584*a(n-7) - 40320*a(n-8) for n>17. - Colin Barker, Jan 05 2018

A271749 Number of set partitions of [n] such that 10 is the largest element of the last block.

Original entry on oeis.org

42294, 168509, 724731, 3321545, 16075611, 81602489, 432156891, 2377526345, 13540170651, 79588371929, 481614364251, 2993757491945, 19079196017691, 124446430190969, 829494189346011, 5642172217982345, 39113680447384731, 276028057609763609, 1980851149371918171

Offset: 10

Alois P. Heinz, Apr 13 2016

Alois P. Heinz, Table of n, a(n) for n = 10..1000
Wikipedia, Partition of a set
Index entries for linear recurrences with constant coefficients, signature (45,-870,9450,-63273,269325,-723680,1172700,-1026576,362880).

Column k=10 of A271466.

Vec(x^10*(42294 - 1734721*x + 29937606*x^2 - 282366820*x^3 + 1580780268*x^4 - 5329525399*x^5 + 10436766264*x^6 - 10665532740*x^7 + 4242318048*x^8 - 362880*x^9) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*x)*(1 - 8*x)*(1 - 9*x)) + O(x^40)) \\ Colin Barker, Jan 05 2018

G.f.: x^10 *(362880*x^9 -4242318048*x^8 +10665532740*x^7 -10436766264*x^6 +5329525399*x^5 -1580780268*x^4 +282366820*x^3 -29937606*x^2 +1734721*x -42294) / Product_{j=1..9} (j*x-1).

a(n) = 45*a(n-1) - 870*a(n-2) + 9450*a(n-3) - 63273*a(n-4) + 269325*a(n-5) - 723680*a(n-6) + 1172700*a(n-7) - 1026576*a(n-8) + 362880*a(n-9) for n>19. - Colin Barker, Jan 05 2018

A271752 Number of set partitions of [n+1] such that n is the largest element of the last block.

Original entry on oeis.org

0, 1, 4, 15, 59, 250, 1145, 5649, 29874, 168509, 1009215, 6391484, 42648083, 298865333, 2193219124, 16811408659, 134289313167, 1115559002906, 9619253991637, 85950089855573, 794567157607386, 7588822028424393, 74783864494826723, 759461721024357540

Offset: 1

Alois P. Heinz, Apr 13 2016

nonn

			a(3) = 4: 124|3, 14|23, 14|2|3, 1|24|3.
a(4) = 15: 1235|4, 125|34, 125|3|4, 12|35|4, 135|24, 135|2|4, 13|25|4, 15|234, 15|23|4, 1|235|4, 15|2|34, 1|25|34, 15|2|3|4, 1|25|3|4, 1|2|35|4.

Alois P. Heinz, Table of n, a(n) for n = 1..576
Wikipedia, Partition of a set

A diagonal of A271466.

a(n) = A271466(n+1,n).

A271753 Number of set partitions of [n+2] such that n is the largest element of the last block.

Original entry on oeis.org

0, 1, 6, 29, 139, 692, 3627, 20085, 117488, 724731, 4703699, 32043002, 228572813, 1703454469, 13235230990, 106997762361, 898404819935, 7821618182572, 70498093658879, 656892909516441, 6319385054660256, 62688326727955007, 640525850674446471, 6733883466256420010

Offset: 1

Alois P. Heinz, Apr 13 2016

nonn

			a(3) = 6: 1245|3, 145|23, 145|2|3, 14|25|3, 15|24|3, 1|245|3.
a(4) = 29: 12356|4, 1256|34, 1256|3|4, 125|36|4, 126|35|4, 12|356|4, 1356|24, 1356|2|4, 135|26|4, 136|25|4, 13|256|4, 156|234, 156|23|4, 15|236|4, 16|235|4, 1|2356|4, 156|2|34, 15|26|34, 16|25|34, 1|256|34, 156|2|3|4, 15|26|3|4, 15|2|36|4, 16|25|3|4, 1|256|3|4, 1|25|36|4, 16|2|35|4, 1|26|35|4, 1|2|356|4.

Alois P. Heinz, Table of n, a(n) for n = 1..575
Wikipedia, Partition of a set

A diagonal of A271466.

a(n) = A271466(n+2,n).

A271754 Number of set partitions of [n+3] such that n is the largest element of the last block.

Original entry on oeis.org

0, 1, 10, 63, 365, 2110, 12521, 77133, 495408, 3321545, 23241681, 169563944, 1288195931, 10176462413, 83473288546, 709925146315, 6251616698625, 56926598141054, 535352734428349, 5193455071192121, 51913950093082800, 534160387907563869, 5651905462025615573

Offset: 1

Alois P. Heinz, Apr 13 2016

nonn

			a(3) = 10: 12456|3, 1456|23, 1456|2|3, 145|26|3, 146|25|3, 14|256|3, 156|24|3, 15|246|3, 16|245|3, 1|2456|3.

Alois P. Heinz, Table of n, a(n) for n = 1..574
Wikipedia, Partition of a set

A diagonal of A271466.

a(n) = A271466(n+3,n).

A271755 Number of set partitions of [n+4] such that n is the largest element of the last block.

Original entry on oeis.org

0, 1, 18, 149, 1039, 6932, 46299, 315597, 2215148, 16075611, 120829511, 941052026, 7592454845, 63417026389, 547926762922, 4892438131137, 45101313988931, 428831073340204, 4201412824028351, 42374784500354529, 439570765566102348, 4685781221854745135

Offset: 1

Alois P. Heinz, Apr 13 2016

nonn

			a(3) = 18: 124567|3, 14567|23, 14567|2|3, 1456|27|3, 1457|26|3, 145|267|3, 1467|25|3, 146|257|3, 147|256|3, 14|2567|3, 1567|24|3, 156|247|3, 157|246|3, 15|2467|3, 167|245|3, 16|2457|3, 17|2456|3, 1|24567|3.

Alois P. Heinz, Table of n, a(n) for n = 1..573
Wikipedia, Partition of a set

A diagonal of A271466.

a(n) = A271466(n+4,n).

A271756 Number of set partitions of [n+5] such that n is the largest element of the last block.

Original entry on oeis.org

0, 1, 34, 375, 3149, 24190, 181265, 1362669, 10419024, 81602489, 657087105, 5449808144, 46591975883, 410650926413, 3730465450474, 34912477523059, 336408561147777, 3335270965246766, 33998967702498997, 356088425256135353, 3829087912372677696

Offset: 1

Alois P. Heinz, Apr 13 2016

nonn

			a(3) = 34: 1245678|3, 145678|23, 145678|2|3, 14567|28|3, 14568|27|3, 1456|278|3, 14578|26|3, 1457|268|3, 1458|267|3, 145|2678|3, 14678|25|3, 1467|258|3, 1468|257|3, 146|2578|3, 1478|256|3, 147|2568|3, 148|2567|3, 14|25678|3, 15678|24|3, 1567|248|3, 1568|247|3, 156|2478|3, 1578|246|3, 157|2468|3, 158|2467|3, 15|24678|3, 1678|245|3, 167|2458|3, 168|2457|3, 16|24578|3, 178|2456|3, 17|24568|3, 18|24567|3, 1|245678|3.

Alois P. Heinz, Table of n, a(n) for n = 1..572
Wikipedia, Partition of a set

A diagonal of A271466.

a(n) = A271466(n+5,n).

A271757 Number of set partitions of [n+6] such that n is the largest element of the last block.

Original entry on oeis.org

0, 1, 66, 989, 10039, 88772, 745107, 6164685, 51235748, 432156891, 3720513359, 32799220082, 296618292653, 2754210931669, 26267172307690, 257304094100601, 2588217808077035, 26724983451319372, 283138925329167239, 3076286737105578561, 34258285168272873876

Offset: 1

Alois P. Heinz, Apr 13 2016

nonn

			a(3) = 66: 12456789|3, 1456789|23, 1456789|2|3, 145678|29|3, 145679|28|3, 14567|289|3, 145689|27|3, 14568|279|3, 14569|278|3, 1456|2789|3, 145789|26|3, 14578|269|3, 14579|268|3, 1457|2689|3, 14589|267|3, 1458|2679|3, 1459|2678|3, 145|26789|3, 146789|25|3, 14678|259|3, 14679|258|3, 1467|2589|3, 14689|257|3, 1468|2579|3, 1469|2578|3, 146|25789|3, 14789|256|3, 1478|2569|3, 1479|2568|3, 147|25689|3, 1489|2567|3, 148|25679|3, 149|25678|3, 14|256789|3, 156789|24|3, 15678|249|3, 15679|248|3, 1567|2489|3, 15689|247|3, 1568|2479|3, 1569|2478|3, 156|24789|3, 15789|246|3, 1578|2469|3, 1579|2468|3, 157|24689|3, 1589|2467|3, 158|24679|3, 159|24678|3, 15|246789|3, 16789|245|3, 1678|2459|3, 1679|2458|3, 167|24589|3, 1689|2457|3, 168|24579|3, 169|24578|3, 16|245789|3, 1789|2456|3, 178|24569|3, 179|24568|3, 17|245689|3, 189|24567|3, 18|245679|3, 19|245678|3, 1|2456789|3.

Alois P. Heinz, Table of n, a(n) for n = 1..571
Wikipedia, Partition of a set

A diagonal of A271466.

a(n) = A271466(n+6,n).

A271758 Number of set partitions of [n+7] such that n is the largest element of the last block.

Original entry on oeis.org

0, 1, 130, 2703, 33365, 340030, 3195161, 29058813, 262138728, 2377526345, 21850848681, 204453592904, 1953119434331, 19080748941293, 190810410926266, 1954112246621755, 20497535793993225, 220206906232309694, 2422414243364061229, 27278730807823249481

Offset: 1

Alois P. Heinz, Apr 13 2016

nonn

			a(2) = 1: 13456789|2.

Alois P. Heinz, Table of n, a(n) for n = 1..570
Wikipedia, Partition of a set

A diagonal of A271466.

a(n) = A271466(n+7,n).

A271759 Number of set partitions of [n+8] such that n is the largest element of the last block.

Original entry on oeis.org

0, 1, 258, 7589, 114799, 1351412, 14220459, 142084077, 1389893708, 13540170651, 132693048551, 1316256290186, 13267436553245, 136223753571349, 1426933424886202, 15263063171191857, 166798075310353571, 1862748034961296684, 21259303294075547951

Offset: 1

Alois P. Heinz, Apr 13 2016

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..569
Wikipedia, Partition of a set

A diagonal of A271466.

a(n) = A271466(n+8,n).

cp's OEIS Frontend

A271748 Number of set partitions of [n] such that 9 is the largest element of the last block.

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A271749 Number of set partitions of [n] such that 10 is the largest element of the last block.

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A271752 Number of set partitions of [n+1] such that n is the largest element of the last block.

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A271753 Number of set partitions of [n+2] such that n is the largest element of the last block.

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A271754 Number of set partitions of [n+3] such that n is the largest element of the last block.

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A271755 Number of set partitions of [n+4] such that n is the largest element of the last block.

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A271756 Number of set partitions of [n+5] such that n is the largest element of the last block.

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A271757 Number of set partitions of [n+6] such that n is the largest element of the last block.

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A271758 Number of set partitions of [n+7] such that n is the largest element of the last block.

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A271759 Number of set partitions of [n+8] such that n is the largest element of the last block.

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