A156225 - OEIS

A156225

Triangle read by rows:e(n,k)=Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}]; t(n,m)=(e[n + 1, m]*PartitionsQ[n] + e[n + 1, n - m]*(PartitionsQ[ n - m] + PartitionsQ[m])) - 2.

1, 1, 1, 1, 10, 1, 3, 42, 42, 3, 3, 128, 262, 128, 3, 5, 340, 1810, 1810, 340, 5, 7, 958, 8335, 19326, 8335, 958, 7, 9, 2468, 38635, 140569, 140569, 38635, 2468, 9, 11, 6022, 160686, 970572, 1561898, 970572, 160686, 6022, 11, 15, 15193, 669758, 6372686

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 12, 90, 524, 4310, 37926, 363362, 3836480, 48184504, 643393254,...}.

LINKS

Table of n, a(n) for n=0..48.

FORMULA

e(n,k)=Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}];

t(n,m)=(e[n + 1, m]*PartitionsQ[n] + e[n + 1, n - m]*(PartitionsQ[ n - m] + PartitionsQ[m])) - 2.

EXAMPLE

{1},

{1, 1},

{1, 10, 1},

{3, 42, 42, 3},

{3, 128, 262, 128, 3},

{5, 340, 1810, 1810, 340, 5},

{7, 958, 8335, 19326, 8335, 958, 7},

{9, 2468, 38635, 140569, 140569, 38635, 2468, 9},

{11, 6022, 160686, 970572, 1561898, 970572, 160686, 6022, 11},

{15, 15193, 669758, 6372686, 17034600, 17034600, 6372686, 669758, 15193, 15},

{19, 38682, 2594827, 37459294, 155809822, 251587966, 155809822, 37459294, 2594827, 38682, 19}

MATHEMATICA

Clear[e, k, t, n, m];

e[n_, k_] = Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}];

t[n_, m_] = (e[n + 1, m]*PartitionsQ[n] + e[n + 1, n - m]*( PartitionsQ[n - m] + PartitionsQ[m])) - 2;

Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A111525 A138261 A068126 * A284327 A322219 A010182

Adjacent sequences: A156222 A156223 A156224 * A156226 A156227 A156228

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 06 2009

STATUS

approved