A095675 -id:A095675 - cp's OEIS frontend

A095676 Row sums of A095675.

1, 5, 28, 179, 1291, 10358, 91337, 876289, 9070546, 100596161, 1188403063, 14881408616, 196696197075, 2734274453061, 39848045797116, 607129121193015, 9646995492421711, 159508268424031670, 2739019526280054917

Offset: 0

N. J. A. Sloane, based on a suggestion from Gary W. Adamson, Jun 22 2004

a[0, 0] = 1; a[n_, 0] := a[n - 1, n - 1]; a[n_, k_] := a[n, k] = If[k < n + 1, a[n, k - 1] + a[n - 1, k - 1], 0]; p[n_, r_] := If[r <= n + 1, Binomial[n, r], 0]; am = Table[ a[n, r], {n, 0, 18}, {r, 0, 18}]; pm = Table[p[n, r], {n, 0, 18}, {r, 0, 18}]; t = am.pm; Plus @@@ t (* Robert G. Wilson v, Jul 12 2004 *)

More terms from Robert G. Wilson v, Jul 13 2004

A095674 Triangle read by rows, formed from product of Pascal's triangle (A007318) and Aitken's (or Bell's) triangle (A011971).

Original entry on oeis.org

1, 2, 2, 5, 7, 5, 15, 22, 25, 15, 52, 74, 97, 97, 52, 203, 277, 372, 449, 411, 203, 877, 1154, 1524, 1948, 2209, 1892, 877, 4140, 5294, 6816, 8734, 10718, 11570, 9402, 4140, 21147, 26441, 33255, 41954, 52357, 62107, 64404, 50127, 21147, 115975, 142416

Offset: 0

N. J. A. Sloane, based on a suggestion from Gary W. Adamson, Jun 22 2004

These triangles are to be thought of as infinite lower-triangular matrices.

			Triangle begins:
1
2 2
5 7 5
15 22 25 15
52 74 97 97 52
203 277 372 449 411 203

Cf. A007318, A011971, A095675. Row sums give A005494. First column is A000110.

a[0, 0] = 1; a[n_, 0] := a[n - 1, n - 1]; a[n_, k_] := a[n, k] = If[k < n + 1, a[n, k - 1] + a[n - 1, k - 1], 0]; p[n_, r_] := If[r <= n + 1, Binomial[n, r], 0]; am = Table[ a[n, r], {n, 0, 9}, {r, 0, 9}]; pm = Table[p[n, r], {n, 0, 9}, {r, 0, 9}]; t = Flatten[pm.am]; Delete[ t, Position[t, 0]] (* Robert G. Wilson v, Jul 12 2004 *)

More terms from Robert G. Wilson v, Jul 13 2004

cp's OEIS Frontend

A095676 Row sums of A095675.

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