A172380 -id:A172380 - cp's OEIS frontend

A172382 Diagonal sums of number triangle A172380.

1, 0, 1, 1, 3, 8, 25, 84, 301, 1139, 4528, 18849, 81968, 371622, 1753164, 8589608, 43624741, 229255133, 1244544545, 6968765313, 40195073827, 238527741350, 1454722738679, 9108812009826, 58503226812174, 385086101416594

Offset: 0

Paul Barry, Feb 01 2010

nonn

a(n+2) gives the diagonal sums of A172381.

A172381 Triangle whose inverse has production matrix with general term (-1)^(n-k+1)*C(k+1, n-k+1).

Original entry on oeis.org

1, 1, 1, 2, 3, 1, 5, 10, 6, 1, 14, 36, 31, 10, 1, 42, 137, 156, 75, 15, 1, 132, 544, 787, 510, 155, 21, 1, 429, 2235, 4017, 3331, 1380, 287, 28, 1, 1430, 9445, 20809, 21405, 11411, 3255, 490, 36, 1, 4862, 40876, 109486, 136921, 90665, 33390, 6916, 786, 45, 1, 16796

Offset: 0

Paul Barry, Feb 01 2010

Product of A033184 and A172380. Diagonal sums are A172382(n+2).

			Triangle begins
1,
1, 1,
2, 3, 1,
5, 10, 6, 1,
14, 36, 31, 10, 1,
42, 137, 156, 75, 15, 1,
132, 544, 787, 510, 155, 21, 1,
429, 2235, 4017, 3331, 1380, 287, 28, 1,
1430, 9445, 20809, 21405, 11411, 3255, 490, 36, 1,
4862, 40876, 109486, 136921, 90665, 33390, 6916, 786, 45, 1,
16796, 180544, 584955, 877252, 704720, 322728, 86443, 13536, 1200, 55, 1
Production array of inverse is
-1, 1,
0, -2, 1,
0, 1, -3, 1,
0, 0, 3, -4, 1,
0, 0, -1, 6, -5, 1,
0, 0, 0, -4, 10, -6, 1,
0, 0, 0, 1, -10, 15, -7, 1,
0, 0, 0, 0, 5, -20, 21, -8, 1,
0, 0, 0, 0, -1, 15, -35, 28, -9, 1,
0, 0, 0, 0, 0, -6, 35, -56, 36, -10, 1,
0, 0, 0, 0, 0, 1, -21, 70, -84, 45, -11, 1

cp's OEIS Frontend

A172382 Diagonal sums of number triangle A172380.

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A172381 Triangle whose inverse has production matrix with general term (-1)^(n-k+1)*C(k+1, n-k+1).

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